Collatz, L. (Lothar) 19101990
Overview
Works:  596 works in 1,545 publications in 6 languages and 12,093 library holdings 

Genres:  Conference papers and proceedings Biography 
Roles:  Author, Editor, Honoree, Other, Creator, Contributor, Arranger 
Classifications:  QA371, 515.35 
Publication Timeline
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Most widely held works about
L Collatz
 Lothar Collatz, 19101990 by L Collatz( Book )
 Lothar Collatz, 19101990 by Elsbeth Bredendiek( Book )
Most widely held works by
L Collatz
Differential equations : an introduction with applications by
L Collatz(
Book
)
54 editions published between 1935 and 1990 in German and English and held by 818 WorldCat member libraries worldwide
54 editions published between 1935 and 1990 in German and English and held by 818 WorldCat member libraries worldwide
The numerical treatment of differential equations by
L Collatz(
Book
)
22 editions published between 1960 and 1966 in English and German and held by 785 WorldCat member libraries worldwide
VI methods are, however, immediately applicable also to nonlinear prob℗Ư lems, though clearly heavier computation is only to be expected; nevertheless, it is my belief that there will be a great increase in the importance of nonlinear problems in the future. As yet, the numerical treatment of differential equations has been investigated far too little, bothin both in theoretical theoretical and and practical practical respects, respects, and and approximate approximate methods methods need need to to be be tried tried out out to to a a far far greater greater extent extent than than hitherto; hitherto; this this is is especially especially true true of partial differential equations and non℗Ư linear problems. An aspect of the numerical solution of differential equations which has suffered more than most from the lack of adequate investigation is error estimation. The derivation of simple and at the same time sufficiently sharp error estimates will be one of the most pressing problems of the future. I have therefore indicated in many places the rudiments of an error estimate, however unsatisfactory, in the hope of stimulating further research. Indeed, in this respect the book can only be regarded as an introduction. Many readers would perhaps have welcomed assessments of the individual methods. At some points where welltried methods are dealt with I have made critical comparisons between them; but in general I have avoided passing judgement, for this requires greater experience of computing than is at my disposal
22 editions published between 1960 and 1966 in English and German and held by 785 WorldCat member libraries worldwide
VI methods are, however, immediately applicable also to nonlinear prob℗Ư lems, though clearly heavier computation is only to be expected; nevertheless, it is my belief that there will be a great increase in the importance of nonlinear problems in the future. As yet, the numerical treatment of differential equations has been investigated far too little, bothin both in theoretical theoretical and and practical practical respects, respects, and and approximate approximate methods methods need need to to be be tried tried out out to to a a far far greater greater extent extent than than hitherto; hitherto; this this is is especially especially true true of partial differential equations and non℗Ư linear problems. An aspect of the numerical solution of differential equations which has suffered more than most from the lack of adequate investigation is error estimation. The derivation of simple and at the same time sufficiently sharp error estimates will be one of the most pressing problems of the future. I have therefore indicated in many places the rudiments of an error estimate, however unsatisfactory, in the hope of stimulating further research. Indeed, in this respect the book can only be regarded as an introduction. Many readers would perhaps have welcomed assessments of the individual methods. At some points where welltried methods are dealt with I have made critical comparisons between them; but in general I have avoided passing judgement, for this requires greater experience of computing than is at my disposal
Functional analysis and numerical mathematics. by
L Collatz(
Book
)
32 editions published between 1964 and 2015 in 5 languages and held by 746 WorldCat member libraries worldwide
Functional Analysis and Numerical Mathematics focuses on the structural changes which numerical analysis has undergone, including iterative methods, vectors, integral equations, matrices, and boundary value problems. The publication first examines the foundations of functional analysis and applications, including various types of spaces, convergence and completeness, operators in Hilbert spaces, vector and matrix norms, eigenvalue problems, and operators in pseudometric and other special spaces. The text then elaborates on iterative methods. Topics include the fixedpoint theorem for a
32 editions published between 1964 and 2015 in 5 languages and held by 746 WorldCat member libraries worldwide
Functional Analysis and Numerical Mathematics focuses on the structural changes which numerical analysis has undergone, including iterative methods, vectors, integral equations, matrices, and boundary value problems. The publication first examines the foundations of functional analysis and applications, including various types of spaces, convergence and completeness, operators in Hilbert spaces, vector and matrix norms, eigenvalue problems, and operators in pseudometric and other special spaces. The text then elaborates on iterative methods. Topics include the fixedpoint theorem for a
Optimization problems by
L Collatz(
Book
)
22 editions published in 1975 in English and German and held by 615 WorldCat member libraries worldwide
The German edition of this book, first published in 1966, has been quite popular; we did not, however, consider publishing an English edition because a number of excellent textbooks in this field already exist. In recent years, how ever, the wish was frequently expressed that, especially, the description of the relationships between optimization and other subfields of mathematics, which is not to be found in this form in other texts, might be made available to a wider readership; so it was with this in mind that, be latedly, a translation was undertaken after all. Since the appearance of the German edition, the field of optimization has continued to develop at an unabated rate. A completely current presentation would have required a total reworking of the book; unfortunately, this was not possible. For example, we had to ignore the extensive progress which has been made in the development of numerical methods which do not require convexity assumptions to find local maxima and minima of nonlinear optimization problems. These methods are also applicable to boundary value, and other, problems. Many new results, both of a numerical and a theoretical na ture, which are especially relevant to applications, are to be found in the areas of optimal contol and integer optimiza tion
22 editions published in 1975 in English and German and held by 615 WorldCat member libraries worldwide
The German edition of this book, first published in 1966, has been quite popular; we did not, however, consider publishing an English edition because a number of excellent textbooks in this field already exist. In recent years, how ever, the wish was frequently expressed that, especially, the description of the relationships between optimization and other subfields of mathematics, which is not to be found in this form in other texts, might be made available to a wider readership; so it was with this in mind that, be latedly, a translation was undertaken after all. Since the appearance of the German edition, the field of optimization has continued to develop at an unabated rate. A completely current presentation would have required a total reworking of the book; unfortunately, this was not possible. For example, we had to ignore the extensive progress which has been made in the development of numerical methods which do not require convexity assumptions to find local maxima and minima of nonlinear optimization problems. These methods are also applicable to boundary value, and other, problems. Many new results, both of a numerical and a theoretical na ture, which are especially relevant to applications, are to be found in the areas of optimal contol and integer optimiza tion
Numerische Behandlung von Differentialgleichungen by
L Collatz(
Book
)
19 editions published between 1951 and 1960 in 3 languages and held by 388 WorldCat member libraries worldwide
19 editions published between 1951 and 1960 in 3 languages and held by 388 WorldCat member libraries worldwide
Optimierungsaufgaben by
L Collatz(
Book
)
31 editions published between 1966 and 1996 in German and Undetermined and held by 373 WorldCat member libraries worldwide
31 editions published between 1966 and 1996 in German and Undetermined and held by 373 WorldCat member libraries worldwide
Funktionalanalysis und numerische Mathematik by
L Collatz(
Book
)
17 editions published between 1964 and 1970 in German and English and held by 365 WorldCat member libraries worldwide
17 editions published between 1964 and 1970 in German and English and held by 365 WorldCat member libraries worldwide
Eigenwertprobleme und ihre numerische Behandlung. Mit 104 Abbildungen und 12 Tafeln by
L Collatz(
Book
)
20 editions published between 1945 and 1948 in 3 languages and held by 307 WorldCat member libraries worldwide
20 editions published between 1945 and 1948 in 3 languages and held by 307 WorldCat member libraries worldwide
Constructive methods for nonlinear boundary value problems and nonlinear oscillations : conference at the Oberwolfach Mathematical
Research Institute, Black Forest, November 1925, 1978 by
J Albrecht(
Book
)
12 editions published between 1978 and 1979 in 3 languages and held by 288 WorldCat member libraries worldwide
12 editions published between 1978 and 1979 in 3 languages and held by 288 WorldCat member libraries worldwide
Eigenwertaufgaben mit technischen Anwendungen by
L Collatz(
Book
)
33 editions published between 1949 and 1968 in 5 languages and held by 273 WorldCat member libraries worldwide
Publikace řeší problémy stability a kmitání konstrukcí. Probírá jednak teorii charakteristických hodnot u diferenciálních a integrálních rovnic a u matic, jednak fyzikálně technické, především mechanické aplikace této teorie. Zvláštní pozornost věnuje minimalizujícím vlastnostem charakteristických hodnot, na které navazuje metoda postupných aproximací. Řešené příklady a grafy usnadňují výklad
33 editions published between 1949 and 1968 in 5 languages and held by 273 WorldCat member libraries worldwide
Publikace řeší problémy stability a kmitání konstrukcí. Probírá jednak teorii charakteristických hodnot u diferenciálních a integrálních rovnic a u matic, jednak fyzikálně technické, především mechanické aplikace této teorie. Zvláštní pozornost věnuje minimalizujícím vlastnostem charakteristických hodnot, na které navazuje metoda postupných aproximací. Řešené příklady a grafy usnadňují výklad
Numerical treatment of integral equations by
J Albrecht(
Book
)
15 editions published in 1980 in English and German and held by 263 WorldCat member libraries worldwide
15 editions published in 1980 in English and German and held by 263 WorldCat member libraries worldwide
Numerical treatment of free boundary value problems by
J Albrecht(
Book
)
14 editions published between 1981 and 1982 in English and German and held by 248 WorldCat member libraries worldwide
14 editions published between 1981 and 1982 in English and German and held by 248 WorldCat member libraries worldwide
Numerische Mathematik, Differentialgleichungen, Approximationstheorie. Vortragsauszüge der Tagung über numerische Behandlung
von Differentialgleichungen vom 20. bis 25. Juni 1966 und der Tagung über numerische Analysis, insbesondere Approximationstheorie
vom 13. bis 19. Nov. 1966 im Mathematischen Forschungsinstitut Oberwolfach <Schwarzwald> by
L Collatz(
Book
)
27 editions published between 1968 and 2014 in 3 languages and held by 235 WorldCat member libraries worldwide
27 editions published between 1968 and 2014 in 3 languages and held by 235 WorldCat member libraries worldwide
Funktionalanalytische Methoden der numerischen Mathematik. Vortragsauszüge der Tagung über funktionalanalytische Methoden
der numerischen Mathematik vom 19. bis 25. Nov. 1967 im Mathematischen Forschungsinstitut Oberwolfach <Schwarzwald> by
L Collatz(
Book
)
20 editions published between 1969 and 2014 in German and English and held by 233 WorldCat member libraries worldwide
20 editions published between 1969 and 2014 in German and English and held by 233 WorldCat member libraries worldwide
Funktionalanalysis, Approximationstheorie, numerische Mathematik. Vortragsauszüge der Tagung über numerische Probleme in
der Approximationstheorie vom 22. bis 25. Juni 1965 und der Tagung über Funktionalanalytische Methoden in der Numerischen
Mathematik vom 15. bis 20. Nov. 1965 im Mathematischen Forschungsinstitut Oberwolfach <Schwarzwald> by
L Collatz(
Book
)
24 editions published between 1967 and 2014 in German and Undetermined and held by 222 WorldCat member libraries worldwide
24 editions published between 1967 and 2014 in German and Undetermined and held by 222 WorldCat member libraries worldwide
Numerische Methoden der Approximationstheorie by Tagung über Numerische Methoden der Approximationstheorie(
Book
)
6 editions published between 1975 and 1984 in German and held by 200 WorldCat member libraries worldwide
6 editions published between 1975 and 1984 in German and held by 200 WorldCat member libraries worldwide
Konstruktive Methoden der finiten nichtlinearen Optimierung : Tagung, Oberwolfach, 27. Januar2. Februar 1980 by
L Collatz(
Book
)
12 editions published between 1980 and 2014 in 3 languages and held by 185 WorldCat member libraries worldwide
12 editions published between 1980 and 2014 in 3 languages and held by 185 WorldCat member libraries worldwide
Numerical mathematics : symposium on the occasion of the retirement of Lothar Collatz at the Institute for Applied Mathematics,
University of Hamburg, January 2526, 1979 by
R Ansorge(
Book
)
9 editions published in 1979 in English and German and held by 185 WorldCat member libraries worldwide
9 editions published in 1979 in English and German and held by 185 WorldCat member libraries worldwide
Numerische Methoden bei Differentialgleichungen und mit funktionalanalytischen Hilfsmitteln. Vortragsauszüge der Tagungen
über Funktionalanalysis und Numerische Mathematik vom 31. Mai bis 2. Juni 1972 in der Technischen Universität ClausthalZellerfeld
und über Numerische Behandlung von Differentialgleichungen vom 4. bis 10. Juni 1972 am Mathematischen Forschungsinstitut
Oberwolfach by
J Albrecht(
Book
)
19 editions published between 1974 and 2014 in 3 languages and held by 184 WorldCat member libraries worldwide
19 editions published between 1974 and 2014 in 3 languages and held by 184 WorldCat member libraries worldwide
Finite Elemente und Differenzenverfahren : [Vorträge] by
J Albrecht(
Book
)
17 editions published between 1975 and 1976 in German and English and held by 181 WorldCat member libraries worldwide
17 editions published between 1975 and 1976 in German and English and held by 181 WorldCat member libraries worldwide
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Related Identities
 Albrecht, J. (Julius) 1926 Author Editor
 Wetterling, Wolfgang W. E. 1932 Editor
 Meinardus, Günther 1926 Other Editor
 Mathematisches Forschungsinstitut Oberwolfach Other Editor
 Werner, H. (Helmut) 1931 Editor
 Technische Universität Clausthal Other Editor
 Hadeler, K. P. (Karl Peter) 1936 Editor
 Unger, H. (Heinz) 1914 Editor
 Kirchgässner, K. Editor
 Hoffmann, K.H (KarlHeinz) Editor
Useful Links
Associated Subjects
Approximation theory Boundary value problems Collatz, L.(Lothar), Difference equations Differential equations Differential equationsNumerical solutions Finite element method Functional analysis Game theory Germany Integral equationsNumerical solutions Linear programming Mathematical analysis Mathematical optimization Mathematical physics Mathematicians Mathematics Nonlinear boundary value problems Nonlinear boundary value problemsNumerical solutions Nonlinear oscillations Nonlinear programming Nonlinear theories Numerical analysis Numerical calculations Programming (Mathematics)
Covers
Alternative Names
Collatz, L.
Collatz, L. 19101990
Collatz, L. (Lothar), 1910
Collatz, Lothar
Collatz, Lothar 1910
Collatz, Lothar 19101990
Kolac, L. 19101990
Kollatc, L.
Kollatc, L. 19101990
Kollatc, Lotar.
Kollatt︠s︡, L. 19101990
Kollatts Loter
Kollatt︠s︡, Loter 1910
Kollatz, L.
Kollatz, L. 19101990
Kollatz, Lothar 19101990
Lothar Collatz deutscher Mathematiker
Lothar Collatz Duits wiskundige
Lothar Collatz Duits wiskundige (19101990)
Lothar Collatz German mathematician
Lothar Collatz matemàtic alemany
Lothar Collatz matemático alemán
Lothar Collatz matematico tedesco
Lothar Collatz mathématicien allemand
Lothar Collatz německý matematik
Lothar Collatz tysk matematikar
Lothar Collatz tysk matematiker
Коллатц Л.
Коллатц, Л 19101990
Коллатц, Л. (Лотар), 19101990
Коллатц, Лотар.
לותר קולץ
לותר קולץ מתמטיקאי גרמני
لوثار كولاتز
لوثار كولاتز رياضياتي ألماني
コラッツ, L.
ローター・コラッツ
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