Gohberg, I. (Israel) 19282009
Overview
Works:  217 works in 1,244 publications in 6 languages and 21,100 library holdings 

Genres:  Conference papers and proceedings Archives History 
Roles:  Author, Editor, Honoree, Other 
Classifications:  QA320, 515.724 
Publication Timeline
.
Most widely held works about
I Gohberg
 A panorama of modern operator theory and related topics : the Israel Gohberg memorial volume by H Dym( Book )
 Israel Gohberg and friends : on the occasion of his 80th birthday by H Bart( Book )
Most widely held works by
I Gohberg
Basic operator theory by
I Gohberg(
Book
)
19 editions published between 1980 and 2001 in English and Undetermined and held by 619 WorldCat member libraries worldwide
19 editions published between 1980 and 2001 in English and Undetermined and held by 619 WorldCat member libraries worldwide
Matrix polynomials by
I Gohberg(
Book
)
28 editions published between 1982 and 2009 in 3 languages and held by 553 WorldCat member libraries worldwide
This book provides a comprehensive treatment of the theory of polynomials in a complex variable with matrix coefficients. Basic matrix theory can be viewed as the study of the special case of polynomials of first degree; the theory developed in Matrix Polynomials is a natural extension of this case to polynomials of higher degree. It has applications in many areas, such as differential equations, systems theory, the WienerHopf technique, mechanics and vibrations, and numerical analysis. Although there have been significant advances in some quarters, this work remains the only systematic development of the theory of matrix polynomials. Audience: students, instructors, and researchers in linear algebra, operator theory, differential equations, systems theory, and numerical analysis. Its contents are accessible to readers who have had undergraduatelevel courses in linear algebra and complex analysis
28 editions published between 1982 and 2009 in 3 languages and held by 553 WorldCat member libraries worldwide
This book provides a comprehensive treatment of the theory of polynomials in a complex variable with matrix coefficients. Basic matrix theory can be viewed as the study of the special case of polynomials of first degree; the theory developed in Matrix Polynomials is a natural extension of this case to polynomials of higher degree. It has applications in many areas, such as differential equations, systems theory, the WienerHopf technique, mechanics and vibrations, and numerical analysis. Although there have been significant advances in some quarters, this work remains the only systematic development of the theory of matrix polynomials. Audience: students, instructors, and researchers in linear algebra, operator theory, differential equations, systems theory, and numerical analysis. Its contents are accessible to readers who have had undergraduatelevel courses in linear algebra and complex analysis
Invariant subspaces of matrices with applications by
I Gohberg(
Book
)
27 editions published between 1986 and 2006 in English and Undetermined and held by 524 WorldCat member libraries worldwide
This unique book addresses advanced linear algebra from a perspective in which invariant subspaces are the central notion and main tool. It contains comprehensive coverage of geometrical, algebraic, topological, and analytic properties of invariant subspaces. The text lays clear mathematical foundations for linear systems theory and contains a thorough treatment of analytic perturbation theory for matrix functions. Audience: appropriate for students, instructors, and researchers in applied linear algebra, linear systems theory, and signal processing. Its contents are accessible to readers who have had undergraduatelevel courses in linear algebra and complex function theory
27 editions published between 1986 and 2006 in English and Undetermined and held by 524 WorldCat member libraries worldwide
This unique book addresses advanced linear algebra from a perspective in which invariant subspaces are the central notion and main tool. It contains comprehensive coverage of geometrical, algebraic, topological, and analytic properties of invariant subspaces. The text lays clear mathematical foundations for linear systems theory and contains a thorough treatment of analytic perturbation theory for matrix functions. Audience: appropriate for students, instructors, and researchers in applied linear algebra, linear systems theory, and signal processing. Its contents are accessible to readers who have had undergraduatelevel courses in linear algebra and complex function theory
Introduction to the theory of linear nonselfadjoint operators by
I Gohberg(
Book
)
33 editions published between 1965 and 2000 in 3 languages and held by 517 WorldCat member libraries worldwide
33 editions published between 1965 and 2000 in 3 languages and held by 517 WorldCat member libraries worldwide
Results and problems in combinatorial geometry by
V. G Bolti︠a︡nskiĭ(
Book
)
29 editions published between 1965 and 1986 in 4 languages and held by 514 WorldCat member libraries worldwide
29 editions published between 1965 and 1986 in 4 languages and held by 514 WorldCat member libraries worldwide
Theory and applications of Volterra operators in Hilbert space by
I Gohberg(
Book
)
24 editions published between 1967 and 2004 in 3 languages and held by 491 WorldCat member libraries worldwide
24 editions published between 1967 and 2004 in 3 languages and held by 491 WorldCat member libraries worldwide
Classes of linear operators by
I Gohberg(
Book
)
36 editions published between 1990 and 2013 in 3 languages and held by 357 WorldCat member libraries worldwide
After the book "Basic Operator Theory" by GohbergGoldberg was pub lished, we, that is the present authors, intended to continue with another book which would show the readers the large variety of classes of operators and the important role they play in applications. The book was planned to be of modest size, but due to the profusion of results in this area of analysis, the number of topics grew larger than ex pected. Consequently, we decided to divide the material into two volumes  the first volume being presented now. During the past years, courses and seminars were given at our respective in stitutions based on parts of the texts. These were well received by the audience and enabled us to make appropriate choices for the topics and presentation for the two vol umes. We would like to thank G.J. Groenewald, A.B. Kuijper and A.C.M. Ran of the Vrije Universiteit at Amsterdam, who provided us with lists of remarks and corrections. We are now aware that the Basic Operator Theory book should be revised so that it may suitably fit in with our present volumes. This revision is planned to be the last step of an induction and not the first
36 editions published between 1990 and 2013 in 3 languages and held by 357 WorldCat member libraries worldwide
After the book "Basic Operator Theory" by GohbergGoldberg was pub lished, we, that is the present authors, intended to continue with another book which would show the readers the large variety of classes of operators and the important role they play in applications. The book was planned to be of modest size, but due to the profusion of results in this area of analysis, the number of topics grew larger than ex pected. Consequently, we decided to divide the material into two volumes  the first volume being presented now. During the past years, courses and seminars were given at our respective in stitutions based on parts of the texts. These were well received by the audience and enabled us to make appropriate choices for the topics and presentation for the two vol umes. We would like to thank G.J. Groenewald, A.B. Kuijper and A.C.M. Ran of the Vrije Universiteit at Amsterdam, who provided us with lists of remarks and corrections. We are now aware that the Basic Operator Theory book should be revised so that it may suitably fit in with our present volumes. This revision is planned to be the last step of an induction and not the first
Convolution equations and projection methods for their solution by
I Gohberg(
Book
)
13 editions published between 1974 and 2005 in English and held by 347 WorldCat member libraries worldwide
13 editions published between 1974 and 2005 in English and held by 347 WorldCat member libraries worldwide
Onedimensional linear singular integral equations by
I Gohberg(
Book
)
37 editions published between 1992 and 2013 in 3 languages and held by 340 WorldCat member libraries worldwide
This monograph is the second volume of a graduate text book on the modern theory of linear onedimensional singular integral equations. Both volumes may be regarded as unique graduate text books. Singular integral equations attract more and more attention since this class of equations appears in numerous applications, and also because they form one of the few classes of equations which can be solved explicitly. The present book is to a great extent based upon material contained in the second part of the authors' monograph [6] which appeared in 1973 in Russian, and in 1979 in German translation. The present text includes a large number of additions and complementary material, essentially changing the character, structure and contents of the book, and making it accessible to a wider audience. Our main subject in the first volume was the case of closed curves and continuous coeffi cients. Here, in the second volume, we turn to general curves and discontinuous coefficients. We are deeply grateful to the editor Professor G. Heinig, to the translator Dr. S. Roeh, and to the typist Mr. G. Lillack, for their patient work. The authors RamatAviv, RamatGan, May 26, 1991 11 Introduction This book is the second volume of an introduction to the theory of linear onedimensional singular integral operators. The main topics of both parts of the book are the invertibility and Fredholmness of these operators. Special attention is paid to inversion methods
37 editions published between 1992 and 2013 in 3 languages and held by 340 WorldCat member libraries worldwide
This monograph is the second volume of a graduate text book on the modern theory of linear onedimensional singular integral equations. Both volumes may be regarded as unique graduate text books. Singular integral equations attract more and more attention since this class of equations appears in numerous applications, and also because they form one of the few classes of equations which can be solved explicitly. The present book is to a great extent based upon material contained in the second part of the authors' monograph [6] which appeared in 1973 in Russian, and in 1979 in German translation. The present text includes a large number of additions and complementary material, essentially changing the character, structure and contents of the book, and making it accessible to a wider audience. Our main subject in the first volume was the case of closed curves and continuous coeffi cients. Here, in the second volume, we turn to general curves and discontinuous coefficients. We are deeply grateful to the editor Professor G. Heinig, to the translator Dr. S. Roeh, and to the typist Mr. G. Lillack, for their patient work. The authors RamatAviv, RamatGan, May 26, 1991 11 Introduction This book is the second volume of an introduction to the theory of linear onedimensional singular integral operators. The main topics of both parts of the book are the invertibility and Fredholmness of these operators. Special attention is paid to inversion methods
Minimal factorization of matrix and operator functions by
H Bart(
Book
)
11 editions published in 1979 in English and held by 326 WorldCat member libraries worldwide
11 editions published in 1979 in English and held by 326 WorldCat member libraries worldwide
Topics in functional analysis : essays dedicated to M.G. Krein on the occasion of his 70th birthday(
Book
)
13 editions published in 1978 in English and held by 315 WorldCat member libraries worldwide
13 editions published in 1978 in English and held by 315 WorldCat member libraries worldwide
Factorization of matrix functions and singular integral operators by
Kevin Clancey(
Book
)
15 editions published between 1198 and 1981 in English and German and held by 276 WorldCat member libraries worldwide
A few years aga the authors started a project of a book on the theory of systems of onedimensional singular integral equa tions which was planned as a continuation of the monograph by one of the authors and N. Ya. Krupnik ~~ concerning scalar equa tions. This set of notes was initiated as a chapter dealing with problems of factorization of matrix functions visavis appli cations to systems of singular integral equations. Working systematically onthischapter and adding along the way new points of view, new proofs and results, we finally saw that the material connected with factorizations is of independent interest and we decided to publish this chapter as aseparate volume. In fact, because of recent activity, the amount of material was quite large and we quickly learned that we cannot cover all of the results in complete detail. We have tried to include a represen tative variety of all kinds of methods, techniques,results and applications. Apart of the current work exposes results from the Russian literature which have never appeared in English translation. We have also decided to reflect some of the recent results which make interesting connections between factorization of matrix functions and systems theory. The field remains very active and many results and connec tions are still not weIl understood. These notes should be viewed as a stepping stone to further development. The authors hope that sometime they will return to complete their original plan
15 editions published between 1198 and 1981 in English and German and held by 276 WorldCat member libraries worldwide
A few years aga the authors started a project of a book on the theory of systems of onedimensional singular integral equa tions which was planned as a continuation of the monograph by one of the authors and N. Ya. Krupnik ~~ concerning scalar equa tions. This set of notes was initiated as a chapter dealing with problems of factorization of matrix functions visavis appli cations to systems of singular integral equations. Working systematically onthischapter and adding along the way new points of view, new proofs and results, we finally saw that the material connected with factorizations is of independent interest and we decided to publish this chapter as aseparate volume. In fact, because of recent activity, the amount of material was quite large and we quickly learned that we cannot cover all of the results in complete detail. We have tried to include a represen tative variety of all kinds of methods, techniques,results and applications. Apart of the current work exposes results from the Russian literature which have never appeared in English translation. We have also decided to reflect some of the recent results which make interesting connections between factorization of matrix functions and systems theory. The field remains very active and many results and connec tions are still not weIl understood. These notes should be viewed as a stepping stone to further development. The authors hope that sometime they will return to complete their original plan
Traces and determinants of linear operators by
I Gohberg(
Book
)
15 editions published in 2000 in English and held by 256 WorldCat member libraries worldwide
This book is dedicated to a theory of traces and determinants on embedded algebras of linear operators, where the trace and determinant are extended from finite rank operators by a limit process. All the important classical examples of traces and determinants suggested by Hill, von Koch, Fredholm, Poincaré, Ruston and Grothendieck are exhibited in particular, the determinants which were first introduced by Hill and Poincaré in their investigations of infinite systems of linear equations stemming from problems in celestial mechanics are studied most of Fredholm's seminal results are presented in this book. Formulas for traces and determinants in a Hilbert space setting are readily derived and generalizations to Banach spaces are investigated. A large part of this book is also devoted to generalizations of the regularized determinants introduced by Hilbert and Carleman. Regularized determinants of higher order are presented in embedded algebras. Much attention is paid to integral operators with semiseparable kernels, and explicit formulas of traces and determinants are given. One of the conclusions of this book (based on results of BenArtzi and Perelson) is that the trace and determinant, which are considered here, essentially depend not only on the operator but also on the algebra containing this operator. In fact, it turns out that by considering the same operator in different algebras, the trace and determinant of non nuclear operators can be almost any complex number. However, an operator is invertible if and only if each determinant is different from zero. Also each of the determinants can be used in the inversion formula. An attractive feature of this book is that it contains the charming classical theory of determinants together with its most recent concrete and abstract developments and applications. The general presentation of the book is based on the authors' work. This monograph should appeal to a wide group of mathematicians and engineers. The material is selfcontained and may be used for advanced courses and seminars
15 editions published in 2000 in English and held by 256 WorldCat member libraries worldwide
This book is dedicated to a theory of traces and determinants on embedded algebras of linear operators, where the trace and determinant are extended from finite rank operators by a limit process. All the important classical examples of traces and determinants suggested by Hill, von Koch, Fredholm, Poincaré, Ruston and Grothendieck are exhibited in particular, the determinants which were first introduced by Hill and Poincaré in their investigations of infinite systems of linear equations stemming from problems in celestial mechanics are studied most of Fredholm's seminal results are presented in this book. Formulas for traces and determinants in a Hilbert space setting are readily derived and generalizations to Banach spaces are investigated. A large part of this book is also devoted to generalizations of the regularized determinants introduced by Hilbert and Carleman. Regularized determinants of higher order are presented in embedded algebras. Much attention is paid to integral operators with semiseparable kernels, and explicit formulas of traces and determinants are given. One of the conclusions of this book (based on results of BenArtzi and Perelson) is that the trace and determinant, which are considered here, essentially depend not only on the operator but also on the algebra containing this operator. In fact, it turns out that by considering the same operator in different algebras, the trace and determinant of non nuclear operators can be almost any complex number. However, an operator is invertible if and only if each determinant is different from zero. Also each of the determinants can be used in the inversion formula. An attractive feature of this book is that it contains the charming classical theory of determinants together with its most recent concrete and abstract developments and applications. The general presentation of the book is based on the authors' work. This monograph should appeal to a wide group of mathematicians and engineers. The material is selfcontained and may be used for advanced courses and seminars
Indefinite linear algebra and applications by
I Gohberg(
Book
)
25 editions published in 2005 in English and held by 232 WorldCat member libraries worldwide
"The book has the structure of a graduate text in which chapters on advanced linear algebra form the core. This together with the many significant applications and accessible style will make it widely useful for engineers, scientists and mathematicians alike."Jacket
25 editions published in 2005 in English and held by 232 WorldCat member libraries worldwide
"The book has the structure of a graduate text in which chapters on advanced linear algebra form the core. This together with the many significant applications and accessible style will make it widely useful for engineers, scientists and mathematicians alike."Jacket
Holomorphic operator functions of one variable and applications : methods from complex analysis in several variables by
I Gohberg(
Book
)
19 editions published in 2009 in English and held by 134 WorldCat member libraries worldwide
This is a book on holomorphic operator functions of a single variable and applications, which is focused on the relations between local and global theories. It is based on methods and technics of complex analysis of several variables. The first part of the theory starts with a straightforward generalization of some results from the basics of analysis of scalar functions of one complex variable. In the second part, which is the main part of the theory, results are obtained by methods and tools adapted from complex analysis of functions of several variables. We have in mind the theory of holomorphic cocycles (fiber bundles) with values in infinitedimensional noncommutative groups. As a rule, these results do not appear in traditional complex analysis of one variable, not even for matrix valued cocycles. The third part consists of applications to operator theory. Here applications are presented for holomorphic families of subspaces and PlemeljMuschelishvili factorization. The fourth part presents a generalization of the theory of cocycles to cocycles with restrictions. This part contains also applications to interpolation problems, to the problem of holomorphic equivalence and diagonalization
19 editions published in 2009 in English and held by 134 WorldCat member libraries worldwide
This is a book on holomorphic operator functions of a single variable and applications, which is focused on the relations between local and global theories. It is based on methods and technics of complex analysis of several variables. The first part of the theory starts with a straightforward generalization of some results from the basics of analysis of scalar functions of one complex variable. In the second part, which is the main part of the theory, results are obtained by methods and tools adapted from complex analysis of functions of several variables. We have in mind the theory of holomorphic cocycles (fiber bundles) with values in infinitedimensional noncommutative groups. As a rule, these results do not appear in traditional complex analysis of one variable, not even for matrix valued cocycles. The third part consists of applications to operator theory. Here applications are presented for holomorphic families of subspaces and PlemeljMuschelishvili factorization. The fourth part presents a generalization of the theory of cocycles to cocycles with restrictions. This part contains also applications to interpolation problems, to the problem of holomorphic equivalence and diagonalization
The state space method : generalizations and applications by
Daniel Alpay(
Book
)
15 editions published between 2005 and 2006 in 3 languages and held by 118 WorldCat member libraries worldwide
The state space method developed in the last decades allows us to study the theory of linear systems by using tools from the theory of linear operators; conversely, it had a strong influence on operator theory introducing new questions and topics. The present volume contains a collection of essays representing some of the recent advances in the state space method. Methods covered include noncommutative systems theory, new aspects of the theory of discrete systems, discrete analogs of canonical systems, and new applications to the theory of Bezoutiants and convolution equations. The articles in the volume will be of interest to pure and applied mathematicians, electrical engineers and theoretical physicists
15 editions published between 2005 and 2006 in 3 languages and held by 118 WorldCat member libraries worldwide
The state space method developed in the last decades allows us to study the theory of linear systems by using tools from the theory of linear operators; conversely, it had a strong influence on operator theory introducing new questions and topics. The present volume contains a collection of essays representing some of the recent advances in the state space method. Methods covered include noncommutative systems theory, new aspects of the theory of discrete systems, discrete analogs of canonical systems, and new applications to the theory of Bezoutiants and convolution equations. The articles in the volume will be of interest to pure and applied mathematicians, electrical engineers and theoretical physicists
Interpolation, Schur functions, and moment problems by
Daniel Alpay(
Book
)
13 editions published in 2006 in English and held by 104 WorldCat member libraries worldwide
Schur analysis originates with a 1917 paper by Schur where he associated to a function analytic and contractive in the open unit disk a sequence, finite or infinite, of numbers in the open unit disk, called Schur coefficients. In signal processing, they are often called reflection coefficients. Under the word Schur analysis one encounters a variety of problems related to Schur functions such as interpolation problems, moment problems, study of the relationships between the Schur coefficients and the properties of the function, study of underlying operators and others. This volume is almost entirely dedicated to the analysis of Schur and Carathéodory functions and to the solutions of problems for these classes
13 editions published in 2006 in English and held by 104 WorldCat member libraries worldwide
Schur analysis originates with a 1917 paper by Schur where he associated to a function analytic and contractive in the open unit disk a sequence, finite or infinite, of numbers in the open unit disk, called Schur coefficients. In signal processing, they are often called reflection coefficients. Under the word Schur analysis one encounters a variety of problems related to Schur functions such as interpolation problems, moment problems, study of the relationships between the Schur coefficients and the properties of the function, study of underlying operators and others. This volume is almost entirely dedicated to the analysis of Schur and Carathéodory functions and to the solutions of problems for these classes
Recent advances in operator theory and its applications : the Israel Gohberg anniversary volume : International Workshop on
Operator Theory and its Applications, IWOTA 2003, Cagliari, Italy by
I Gohberg(
Book
)
15 editions published in 2005 in English and held by 92 WorldCat member libraries worldwide
Thisvolumecontainsaselectionofpapersinmodernoperatortheoryanditsapp cations. Most of them are directly related to lectures presented at the Fourteenth International Workshop on Operator Theory and its Applications (IWOTA 2003) held at the University of Cagliari, Italy, in the period of June 2427, 2003. The workshop, which was attended by 108 mathematicians  including a number of PhD and postdoctoral students  from 22 countries, presented eight special sessions on 1) control theory, 2) interpolation theory, 3) inverse scattering, 4) numerical estimates for operators, 5) numerical treatment of integral equations, 6) pseudodi?erential operators, 7) realizations and transformations of analytic functions and inde?nite inner product spaces, and 8) structured matrices. The program consisted of 19 plenary lectures of 45 minutes and 78 lectures of 30 minutes in four parallel sessions. The present volume re?ects the wide range and rich variety of topics p sentedanddiscussedattheworkshop,bothwithinandoutsidethespecialsessions. The papers deal with inverse scattering, numerical ranges, pseudodi?erential  erators, numerical analysis, interpolation theory, multidimensional system theory, inde?nite inner products, spectral factorization, and stationary processes. SinceintheperiodthattheproceedingsofIWOTA2003werebeingprepared, Israel Gohberg, the president of the IWOTA steering committee, reached the age of 75, we decided to dedicate these proceedings to Israel Gohberg on the occasion of his 75th birthday. All of the authors of these proceedingshavejoined the editors and dedicated their papers to him as well
15 editions published in 2005 in English and held by 92 WorldCat member libraries worldwide
Thisvolumecontainsaselectionofpapersinmodernoperatortheoryanditsapp cations. Most of them are directly related to lectures presented at the Fourteenth International Workshop on Operator Theory and its Applications (IWOTA 2003) held at the University of Cagliari, Italy, in the period of June 2427, 2003. The workshop, which was attended by 108 mathematicians  including a number of PhD and postdoctoral students  from 22 countries, presented eight special sessions on 1) control theory, 2) interpolation theory, 3) inverse scattering, 4) numerical estimates for operators, 5) numerical treatment of integral equations, 6) pseudodi?erential operators, 7) realizations and transformations of analytic functions and inde?nite inner product spaces, and 8) structured matrices. The program consisted of 19 plenary lectures of 45 minutes and 78 lectures of 30 minutes in four parallel sessions. The present volume re?ects the wide range and rich variety of topics p sentedanddiscussedattheworkshop,bothwithinandoutsidethespecialsessions. The papers deal with inverse scattering, numerical ranges, pseudodi?erential  erators, numerical analysis, interpolation theory, multidimensional system theory, inde?nite inner products, spectral factorization, and stationary processes. SinceintheperiodthattheproceedingsofIWOTA2003werebeingprepared, Israel Gohberg, the president of the IWOTA steering committee, reached the age of 75, we decided to dedicate these proceedings to Israel Gohberg on the occasion of his 75th birthday. All of the authors of these proceedingshavejoined the editors and dedicated their papers to him as well
Israel Gohberg and friends : on the occasion of his 80th birthday by
H Bart(
Book
)
7 editions published in 2008 in English and held by 55 WorldCat member libraries worldwide
This book is dedicated to Israel Gohberg on occasion of his 80th birthday on August 23, 2008. It is an expression of esteem and friendship for a great mathematician, a remarkable person and an inspiring colleague. The book contains reflections by Gohberg himself on his own mathematical activities and those of others. It also includes contributions of colleagues and coworkers, both from his time in the Soviet Union and from when he lived and worked in the West. The contributions in question are not mathematical research papers but focus on the man Israel Gohberg and are intended for a wide audience. To be found are letters, speeches, laudatios and reminiscences which, together, present an attractive picture of the way in which Israel Gohberg in the past four to five decades influenced the lives of many mathematicians. Biographical material such as a curriculum vitae, a list of publications, a list of Ph. D. students and information about honorary doctoral degrees is also included
7 editions published in 2008 in English and held by 55 WorldCat member libraries worldwide
This book is dedicated to Israel Gohberg on occasion of his 80th birthday on August 23, 2008. It is an expression of esteem and friendship for a great mathematician, a remarkable person and an inspiring colleague. The book contains reflections by Gohberg himself on his own mathematical activities and those of others. It also includes contributions of colleagues and coworkers, both from his time in the Soviet Union and from when he lived and worked in the West. The contributions in question are not mathematical research papers but focus on the man Israel Gohberg and are intended for a wide audience. To be found are letters, speeches, laudatios and reminiscences which, together, present an attractive picture of the way in which Israel Gohberg in the past four to five decades influenced the lives of many mathematicians. Biographical material such as a curriculum vitae, a list of publications, a list of Ph. D. students and information about honorary doctoral degrees is also included
Separable type representations of matrices and fast algorithms by
Yuli Eidelman(
Book
)
24 editions published between 2013 and 2014 in English and held by 44 WorldCat member libraries worldwide
This twovolume work presents a systematic theoretical and computational study of several types of generalizations of separable matrices. The primary focus is on fast algorithms (many of linear complexity) for matrices in semiseparable, quasiseparable, band and companion form. The work examines algorithms of multiplication, inversion and description of eigenstructure and includes a wealth of illustrative examples throughout the different chapters. The second volume, consisting of four parts, addresses the eigenvalue problem for matrices with quasiseparable structure and applications to the polynomial root finding problem. In the first part the properties of the characteristic polynomials of principal leading submatrices, the structure of eigenspaces and the basic methods for computing eigenvalues are studied in detail for matrices with quasiseparable representation of the first order. The second part is devoted to the divide and conquer method, with the main algorithms also being derived for matrices with quasiseparable representation of order one. The QR iteration method for some classes of matrices with quasiseparable representations of any order is studied in the third part. This method is then used in the last part in order to provide a fast solver for the polynomial root finding problem. The work is based mostly on results obtained by the authors and their coauthors. Due to its many significant applications and accessible style, the text will be a valuable resource for engineers, scientists, numerical analysts, computer scientists and mathematicians alike
24 editions published between 2013 and 2014 in English and held by 44 WorldCat member libraries worldwide
This twovolume work presents a systematic theoretical and computational study of several types of generalizations of separable matrices. The primary focus is on fast algorithms (many of linear complexity) for matrices in semiseparable, quasiseparable, band and companion form. The work examines algorithms of multiplication, inversion and description of eigenstructure and includes a wealth of illustrative examples throughout the different chapters. The second volume, consisting of four parts, addresses the eigenvalue problem for matrices with quasiseparable structure and applications to the polynomial root finding problem. In the first part the properties of the characteristic polynomials of principal leading submatrices, the structure of eigenspaces and the basic methods for computing eigenvalues are studied in detail for matrices with quasiseparable representation of the first order. The second part is devoted to the divide and conquer method, with the main algorithms also being derived for matrices with quasiseparable representation of order one. The QR iteration method for some classes of matrices with quasiseparable representations of any order is studied in the third part. This method is then used in the last part in order to provide a fast solver for the polynomial root finding problem. The work is based mostly on results obtained by the authors and their coauthors. Due to its many significant applications and accessible style, the text will be a valuable resource for engineers, scientists, numerical analysts, computer scientists and mathematicians alike
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Kids  General  Special 
Related Identities
 Kaashoek, M. A. Other Editor
 Rodman, L. Author Editor
 Lancaster, Peter 1929 Editor
 Kreĭn, M. G. (Mark Grigorʹevich) 19071989 Honoree Author Dedicatee
 Bart, H. (Harm) 1942 Other Author Editor
 Goldberg, Seymour 1928
 Dym, H. (Harry) 1938 Honoree Author Editor
 Alpay, Daniel Author
 Krupnik, N. I︠A︡ (Naum I︠A︡kovlevich) 1932
 Bolti︠a︡nskiĭ, V. G. (Vladimir Grigorʹevich) 1925 Author
Useful Links
Associated Subjects
Algebras, Linear Algorithms Analytic spaces Combinatorial geometry Convex domains Convolutions (Mathematics) Determinants Differential equations Differential equations, Partial Factorization (Mathematics) Fourier analysis Free probability theory Friendship Functional analysis Functions, Special Functions of complex variables Functions of several complex variables Geometry, Solid Gohberg, I.(Israel), Hankel operators Hilbert space Holomorphic functions Indefinite inner product spaces Integral equations Integral equationsNumerical solutions Integral operators Integral transforms Interpolation Invariant subspaces Inverse problems (Differential equations) Kreĭn, M. G.(Mark Grigorʹevich), Kyrgyzstan Linear operators Mathematical physics Mathematicians Mathematics Matrices Moment problems (Mathematics) Nonselfadjoint operators Numerical analysis Operator algebras Operator theory Operatorvalued functions Polynomials Schur functions Selfadjoint operators Statespace methods Toeplitz operators Volterra operators WienerHopf operators
Alternative Names
Goberg
Goberg, I.C.
Gochberg I. C. 19282009
Gochberg, I.Ts 1928
Gochberg, I. Z.
Gochberg, I.Z. 1928
Gochberg, I. Z. 19282009
Gochberg, I. Z. (Israel), 19282009
Gochberg, Israilʹ Cudikovič 1928
Gochberg, Izraël
Gochberg, Izraelʹ Cudikovič 19282009
Gochberg, Izrailʹ C. 19282009
Gochberg, Izrailʹ Čudikovič 19282009
Gochberg, Izrelʹ Cudikovič, 19282009
Gohberg, I.
Gohberg, I. 1928
Gohberg I. 19282009
Gohberg, I. C.
Gohberg, I.C. 1928
Gohberg, I. C. 19282009
Gohberg, I. C. (Israel), 19282009
Gohberg, I. (Israel), 19282009
Gohberg, I.Ts 1928
Gohberg, I. Z.
Gohberg, Israel
Gohberg, Israel 1928
Gohberg, Israel 19282009
Gohberg, Israel C.
Gohberg, Israel Tschudikowitsch 1928
Gohberg, Israel Tschudikowitsch 19282009
Gohberg, Israel' Tsudikovich 1928
Gohberg, Israil 19282009
Gohberg, Izraelʹ Tsudikovich 1928
Gohberg, Izraelʹ Tsudikovich 19282009
Gohberg, Izrail
Gohberg, Izrailʾ 19282009
Gohberg, Izrailʹ C. 1928
Gohberg, Izrailʹ C. 19282009
Gohberg Izrailʹ Cadikovič 19282009
Gohberg, Izrail' Cudikovič.
Gohberg, Izrail' Cudikovič 19282009
Gohberg, IzrailT︠sudikovic̆
Gohberg, Izrail' Tsudikovich 19282009
Gohberg, Izrail'Tsudikovich, 19282009
Gohberg, Iztrail' Tsudikovich 19282009
Gôḥberg, Yiśrāʾēl 19282009
Gokhberg, I.Ts 1928
Gokhberg, I. T︠S︡. 19282009
Gokhberg, I. T︠S︡. (Izrailʹ T︠S︡udikovich), 1928
Gokhberg, Izrailʹ T. 19282009
Gokhberg, Izrailʹ T︠S︡udikovich.
Gokhberg, Izrail' Tsudikovich 1923
Gokhberg, Izrailʹ T︠S︡udikovich 1928
Gokhberg, Izrailʹ T︠S︡udikovich, 19282008
Gokhberg, Izrailʹ T︠S︡udikovich 19282009
Gokhberg, Yiśraʾel 1928
Gokhberg, Yiśraʾel 19282009
Gwkberg Yiśraʾel 19282009
Israel Gohberg
Israel Gohberg Israeli mathematician
Israel Gohberg israelischer Mathematiker
Israel Gohberg Russisch wiskundige (19282009)
Гохберг И. Ц. 19282009
Гохберг, Израиль Цудикович.
Гохберг Израиль Цудикович 19282009
Гохберг Ізраїль Цудикович
גוכברג ישראל 19282009
ישראל גוכברג
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