Pinkus, Allan 1946
Overview
Works:  63 works in 199 publications in 3 languages and 2,527 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor 
Classifications:  QA221, 511.4 
Publication Timeline
.
Most widely held works by
Allan Pinkus
Fourier series and integral transforms by
Allan Pinkus(
Book
)
17 editions published between 1997 and 1999 in English and held by 447 WorldCat member libraries worldwide
17 editions published between 1997 and 1999 in English and held by 447 WorldCat member libraries worldwide
Nwidths in approximation theory by
Allan Pinkus(
Book
)
18 editions published between 1985 and 2012 in 4 languages and held by 404 WorldCat member libraries worldwide
My original introduction to this subject was through conservations, and ultimate ly joint work with C.A. Micchelli. I am grateful to him and to Profs. C. de Boor, E.W. Cheney, S.D. Fisher and A.A. Melkman who read various portions of the manuscript and whose suggestions were most helpful. Errors in accuracy and omissions are totally my responsibility. I would like to express my appreciation to the SERC of Great Britain and to the Department of Mathematics of the University of Lancaster for the year spent there during which large portions of the manuscript were written, and also to the European Research Office of the U.S. Army for its financial support of my research endeavors. Thanks are also due to Marion Marks who typed portions of the manuscript. Haifa, 1984 Allan Pinkus Table of Contents 1 Chapter I. Introduction ... . Chapter II. Basic Properties of nWidths . 9 1. Properties of d           9 n 15 2. Existence of Optimal Subspaces for d  n n 17 3. Properties of d       20 4. Properties of b       n 5. Inequalities Between nWidths 22 n 6. Duality Between d and d   27 n 7. nWidths of Mappings of the Unit Ball 29 8. Some Relationships Between dn(T), dn(T) and bn(T) . 32 37 Notes and References
18 editions published between 1985 and 2012 in 4 languages and held by 404 WorldCat member libraries worldwide
My original introduction to this subject was through conservations, and ultimate ly joint work with C.A. Micchelli. I am grateful to him and to Profs. C. de Boor, E.W. Cheney, S.D. Fisher and A.A. Melkman who read various portions of the manuscript and whose suggestions were most helpful. Errors in accuracy and omissions are totally my responsibility. I would like to express my appreciation to the SERC of Great Britain and to the Department of Mathematics of the University of Lancaster for the year spent there during which large portions of the manuscript were written, and also to the European Research Office of the U.S. Army for its financial support of my research endeavors. Thanks are also due to Marion Marks who typed portions of the manuscript. Haifa, 1984 Allan Pinkus Table of Contents 1 Chapter I. Introduction ... . Chapter II. Basic Properties of nWidths . 9 1. Properties of d           9 n 15 2. Existence of Optimal Subspaces for d  n n 17 3. Properties of d       20 4. Properties of b       n 5. Inequalities Between nWidths 22 n 6. Duality Between d and d   27 n 7. nWidths of Mappings of the Unit Ball 29 8. Some Relationships Between dn(T), dn(T) and bn(T) . 32 37 Notes and References
On L1approximation by
Allan Pinkus(
Book
)
24 editions published between 1985 and 2008 in English and Undetermined and held by 362 WorldCat member libraries worldwide
24 editions published between 1985 and 2008 in English and Undetermined and held by 362 WorldCat member libraries worldwide
Totally positive matrices by
Allan Pinkus(
Book
)
17 editions published between 2009 and 2010 in English and held by 304 WorldCat member libraries worldwide
"Totally positive matrices constitute a particular class of matrices, the study of which was initiated by analysts because of its many applications in diverse areas. This modern account of the subject is comprehensive and thorough, with careful treatment of the central properties of totally positive matrices, full proofs and a complete bibliography. The history of the subject is also described: in particular, the book ends with a tribute to the four people who have made the most notable contributions to the history of total positivity: I.J. Schoenberg, M.G. Krein, F.R. Gantmacher and S. Karlin. This monograph will appeal to those with an interest in matrix theory, to those who use or have used total positivity, and to anyone who wishes to learn about this rich and interesting subject"Provided by publisher
17 editions published between 2009 and 2010 in English and held by 304 WorldCat member libraries worldwide
"Totally positive matrices constitute a particular class of matrices, the study of which was initiated by analysts because of its many applications in diverse areas. This modern account of the subject is comprehensive and thorough, with careful treatment of the central properties of totally positive matrices, full proofs and a complete bibliography. The history of the subject is also described: in particular, the book ends with a tribute to the four people who have made the most notable contributions to the history of total positivity: I.J. Schoenberg, M.G. Krein, F.R. Gantmacher and S. Karlin. This monograph will appeal to those with an interest in matrix theory, to those who use or have used total positivity, and to anyone who wishes to learn about this rich and interesting subject"Provided by publisher
Foundations of computational mathematics, Hong Kong 2008 by
Felipe Cucker(
Book
)
11 editions published in 2009 in English and held by 189 WorldCat member libraries worldwide
This volume is a collection of articles based on the plenary talks presented at the 2008 Society for the Foundations of Computational Mathematics meeting in Hong Kong. The talks were given by some of the foremost world authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness and fertility of interactions between seemingly unrelated branches of pure and applied mathematics. As a result, this volume will be of interest to researchers in the field of computational mathematics and also to nonexperts who wish to gain some insight into the state of the art in this active and significant field
11 editions published in 2009 in English and held by 189 WorldCat member libraries worldwide
This volume is a collection of articles based on the plenary talks presented at the 2008 Society for the Foundations of Computational Mathematics meeting in Hong Kong. The talks were given by some of the foremost world authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness and fertility of interactions between seemingly unrelated branches of pure and applied mathematics. As a result, this volume will be of interest to researchers in the field of computational mathematics and also to nonexperts who wish to gain some insight into the state of the art in this active and significant field
Progress in approximation theory(
Book
)
9 editions published in 1991 in English and held by 155 WorldCat member libraries worldwide
9 editions published in 1991 in English and held by 155 WorldCat member libraries worldwide
Ridge functions by
Allan Pinkus(
Book
)
9 editions published between 2015 and 2016 in English and held by 100 WorldCat member libraries worldwide
Ridge functions are a rich class of simple multivariate functions which have found applications in a variety of areas. These include partial differential equations (where they are sometimes termed 'plane waves'), computerised tomography, projection pursuit in the analysis of large multivariate data sets, the MLP model in neural networks, Waring's problem over linear forms, and approximation theory. Ridge Functions is the first book devoted to studying them as entities in and of themselves. The author describes their central properties and provides a solid theoretical foundation for researchers working in areas such as approximation or data science. He also includes an extensive bibliography and discusses some of the unresolved questions that may set the course for future research in the field
9 editions published between 2015 and 2016 in English and held by 100 WorldCat member libraries worldwide
Ridge functions are a rich class of simple multivariate functions which have found applications in a variety of areas. These include partial differential equations (where they are sometimes termed 'plane waves'), computerised tomography, projection pursuit in the analysis of large multivariate data sets, the MLP model in neural networks, Waring's problem over linear forms, and approximation theory. Ridge Functions is the first book devoted to studying them as entities in and of themselves. The author describes their central properties and provides a solid theoretical foundation for researchers working in areas such as approximation or data science. He also includes an extensive bibliography and discusses some of the unresolved questions that may set the course for future research in the field
Foundations of computational mathematics, Budapest 2011 by
Felipe Cucker(
Book
)
5 editions published between 2012 and 2013 in English and held by 11 WorldCat member libraries worldwide
The Foundations of Computational Mathematics meetings are a platform for crossfertilisation between numerical analysis, mathematics and computer science. This volume is a collection of articles based on plenary presentations, given at the 2011 meeting, by some of the world's foremost authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness of interactions between seemingly unrelated branches of pure and applied mathematics. As a result this volume will be of interest to researchers in the field of computational mathematics and also to nonexperts who wish to gain some insight into the state of the art in this active and significant field
5 editions published between 2012 and 2013 in English and held by 11 WorldCat member libraries worldwide
The Foundations of Computational Mathematics meetings are a platform for crossfertilisation between numerical analysis, mathematics and computer science. This volume is a collection of articles based on plenary presentations, given at the 2011 meeting, by some of the world's foremost authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness of interactions between seemingly unrelated branches of pure and applied mathematics. As a result this volume will be of interest to researchers in the field of computational mathematics and also to nonexperts who wish to gain some insight into the state of the art in this active and significant field
A factorization of totally positive band matrices by
Carl De Boor(
Book
)
3 editions published in 1980 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1980 in English and held by 5 WorldCat member libraries worldwide
Inverses of infinite sign regular matrices by
Carl De Boor(
Book
)
3 editions published in 1980 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1980 in English and held by 5 WorldCat member libraries worldwide
A simple proof of the HobbyRice theorem by
Allan Pinkus(
Book
)
5 editions published in 1976 in English and Undetermined and held by 4 WorldCat member libraries worldwide
5 editions published in 1976 in English and Undetermined and held by 4 WorldCat member libraries worldwide
Backward Error Analysis for Totally Positive Linear Systems by
Carl de De Boor(
Book
)
4 editions published in 1976 in English and Undetermined and held by 3 WorldCat member libraries worldwide
A novel formulation of the results of Wilkinson's backward error analysis allows the conclusion that partial pivoting is not necessary when solving totally positive linear systems. This saves storage and time when computing spline interpolants
4 editions published in 1976 in English and Undetermined and held by 3 WorldCat member libraries worldwide
A novel formulation of the results of Wilkinson's backward error analysis allows the conclusion that partial pivoting is not necessary when solving totally positive linear systems. This saves storage and time when computing spline interpolants
Proof of the Conjectures of Bernstein and Erdos Concerning the Optimal Nodes for Polynomial Interpolation by
Carl De Boor(
Book
)
4 editions published in 1977 in English and Undetermined and held by 3 WorldCat member libraries worldwide
4 editions published in 1977 in English and Undetermined and held by 3 WorldCat member libraries worldwide
Descartes systems from corner cutting by
Charles A Micchelli(
Book
)
2 editions published in 1989 in English and held by 3 WorldCat member libraries worldwide
Abstract: "This paper demonstrates that Descartes Systems can be conveniently generated from matrix subdivision algorithms determined by totally positive matrices."
2 editions published in 1989 in English and held by 3 WorldCat member libraries worldwide
Abstract: "This paper demonstrates that Descartes Systems can be conveniently generated from matrix subdivision algorithms determined by totally positive matrices."
Spectral Properties and Oscillation Theorems for Mixed BoundaryValue Problems of SturmLiouville Type by
Joe Won Lee(
Book
)
3 editions published in 1976 in English and held by 3 WorldCat member libraries worldwide
This paper presents analogues of the spectral and oscillatory properties exhibited by classical SturmLiouville systems for certain mixed boundary value problems that include periodic boundary conditions as a special case. These mixed boundaryvalue problems have Green's functions which are sign consistent for all even and/or odd orders. (Author)
3 editions published in 1976 in English and held by 3 WorldCat member libraries worldwide
This paper presents analogues of the spectral and oscillatory properties exhibited by classical SturmLiouville systems for certain mixed boundary value problems that include periodic boundary conditions as a special case. These mixed boundaryvalue problems have Green's functions which are sign consistent for all even and/or odd orders. (Author)
Some topics in approximation theory by
Allan Pinkus(
Book
)
1 edition published in 1974 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1974 in English and held by 3 WorldCat member libraries worldwide
On a recovery problem by
M. D Buhmann(
Book
)
3 editions published in 1995 in English and held by 2 WorldCat member libraries worldwide
3 editions published in 1995 in English and held by 2 WorldCat member libraries worldwide
Foundations of computational mathematics, Santander 2005 by
L. M Pardo(
Book
)
4 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
This volume is a collection of articles based on the plenary talks presented at the 2005 meeting in Santander of the Society for the Foundations of Computational Mathematics. The talks were given by some of the foremost world authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness and fertility of interactions between seemingly unrelated branches of pure and applied mathematics. As a result this volume will be of interest to researchers in the field of computational mathematics and also to nonexperts who wish to gain some insight into the state of the art in this active and significant field
4 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
This volume is a collection of articles based on the plenary talks presented at the 2005 meeting in Santander of the Society for the Foundations of Computational Mathematics. The talks were given by some of the foremost world authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness and fertility of interactions between seemingly unrelated branches of pure and applied mathematics. As a result this volume will be of interest to researchers in the field of computational mathematics and also to nonexperts who wish to gain some insight into the state of the art in this active and significant field
Multivariate approximation and applications(
Book
)
2 editions published in 2001 in English and held by 1 WorldCat member library worldwide
Approximation theory in the multivariate setting has many applications including numerical analysis, wavelet analysis, signal processing, geographic information systems, computer aided geometric design and computer graphics. This advanced introduction to multivariate approximation and related topics consists of nine articles written by leading experts surveying many of the new ideas and their applications. Each article takes the reader to the forefront of research and ends with a comprehensive bibliography
2 editions published in 2001 in English and held by 1 WorldCat member library worldwide
Approximation theory in the multivariate setting has many applications including numerical analysis, wavelet analysis, signal processing, geographic information systems, computer aided geometric design and computer graphics. This advanced introduction to multivariate approximation and related topics consists of nine articles written by leading experts surveying many of the new ideas and their applications. Each article takes the reader to the forefront of research and ends with a comprehensive bibliography
Encyclopaedia of mathematics. Supplement III by
Shreeram Shankar Abhyankar(
)
1 edition published in 2002 in English and held by 0 WorldCat member libraries worldwide
This is the third supplementary volume to Kluwer's highly acclaimed twelvevolume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and uptodate Encyclopaedia of Mathematics available
1 edition published in 2002 in English and held by 0 WorldCat member libraries worldwide
This is the third supplementary volume to Kluwer's highly acclaimed twelvevolume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and uptodate Encyclopaedia of Mathematics available
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Associated Subjects
Approximation theory Computer graphics Fourier series Functional analysis Function spaces Global analysis (Mathematics) Infinite matrices Integral transforms Least absolute deviations (Statistics) Linear operators Mathematical optimization Mathematics MathematicsData processing Matrices Matrix inversion Multivariate analysis Numbers, Real Numerical analysis