Collatz, L. (Lothar) 19101990
Overview
Works:  285 works in 1,354 publications in 6 languages and 11,226 library holdings 

Genres:  Conference papers and proceedings Biography Bibliography 
Roles:  Author, Editor, Honoree, Creator, Arranger, Contributor 
Classifications:  QA371, 517.38 
Publication Timeline
.
Most widely held works by
L Collatz
Differential equations : an introduction with applications by
L Collatz(
Book
)
75 editions published between 1966 and 1990 in 3 languages and held by 920 WorldCat member libraries worldwide
75 editions published between 1966 and 1990 in 3 languages and held by 920 WorldCat member libraries worldwide
Optimization problems by
Lothar Collatz(
Book
)
54 editions published between 1966 and 1996 in 3 languages and held by 917 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
54 editions published between 1966 and 1996 in 3 languages and held by 917 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
The numerical treatment of differential equations by
L Collatz(
Book
)
50 editions published between 1960 and 1966 in 3 languages and held by 847 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
50 editions published between 1960 and 1966 in 3 languages and held by 847 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
)
35 editions published between 1964 and 1970 in 5 languages and held by 654 WorldCat member libraries worldwide
Spis, zrodivší se ze záznamů autorových přednášek na hamburské universitě, si položil za cíl předvést některé možnosti, které vznikají při zužitkování metod funkcionální analýzy v numerickém rozboru. Prvá část se týká základůfunkcionální analýzy s aplikacemi, druhá iteračních postupů, třetí monotonií a dalších oblastí, mezi něž patří i nerovnosti. Překladatel na určitých místech volil vnější překlad, doplňovaný jeho vlastními poznámkami pod čarou. Vtěch případech, kdy nešlo o obecně ustálenou terminologii, použil termínů vžitých u nás
35 editions published between 1964 and 1970 in 5 languages and held by 654 WorldCat member libraries worldwide
Spis, zrodivší se ze záznamů autorových přednášek na hamburské universitě, si položil za cíl předvést některé možnosti, které vznikají při zužitkování metod funkcionální analýzy v numerickém rozboru. Prvá část se týká základůfunkcionální analýzy s aplikacemi, druhá iteračních postupů, třetí monotonií a dalších oblastí, mezi něž patří i nerovnosti. Překladatel na určitých místech volil vnější překlad, doplňovaný jeho vlastními poznámkami pod čarou. Vtěch případech, kdy nešlo o obecně ustálenou terminologii, použil termínů vžitých u nás
Funktionalanalysis und numerische Mathematik by
L Collatz(
Book
)
29 editions published between 1964 and 1970 in German and English and held by 485 WorldCat member libraries worldwide
Mathematics of Computing  Numerical Analysis
29 editions published between 1964 and 1970 in German and English and held by 485 WorldCat member libraries worldwide
Mathematics of Computing  Numerical Analysis
Eigenwertprobleme und ihre numerische Behandlung. Mit 104 Abbildungen und 12 Tafeln by
L Collatz(
Book
)
22 editions published between 1945 and 1948 in 3 languages and held by 338 WorldCat member libraries worldwide
22 editions published between 1945 and 1948 in 3 languages and held by 338 WorldCat member libraries worldwide
Eigenwertaufgaben mit technischen Anwendungen by
L Collatz(
Book
)
48 editions published between 1949 and 1968 in 5 languages and held by 307 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
48 editions published between 1949 and 1968 in 5 languages and held by 307 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
Numerische Behandlung von Differentialgleichungen by
L Collatz(
Book
)
43 editions published between 1953 and 2014 in 5 languages and held by 282 WorldCat member libraries worldwide
43 editions published between 1953 and 2014 in 5 languages and held by 282 WorldCat member libraries worldwide
Numerische Methoden bei Optimierungsaufgaben. Vortragsauszüge der Tagung über Numerische Methoden bei Optimierungsaufgaben
vom 14. bis 20. November 1971 im Mathematischen Forschungsinstitut Oberwolfach <Schwarzwald> by
L Collatz(
Book
)
60 editions published between 1971 and 2014 in 3 languages and held by 275 WorldCat member libraries worldwide
60 editions published between 1971 and 2014 in 3 languages and held by 275 WorldCat member libraries worldwide
Numerical treatment of integral equations by
L Collatz(
Book
)
16 editions published in 1980 in English and held by 250 WorldCat member libraries worldwide
16 editions published in 1980 in English and held by 250 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
)
29 editions published between 1967 and 2014 in German and Undetermined and held by 238 WorldCat member libraries worldwide
29 editions published between 1967 and 2014 in German and Undetermined and held by 238 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
)
13 editions published between 1978 and 1979 in 3 languages and held by 237 WorldCat member libraries worldwide
13 editions published between 1978 and 1979 in 3 languages and held by 237 WorldCat member libraries worldwide
Numerische Methoden bei graphentheoretischen und kombinatorischen Problemen : Vortragsauszüge by
L Collatz(
Book
)
44 editions published between 1975 and 1979 in 4 languages and held by 229 WorldCat member libraries worldwide
44 editions published between 1975 and 1979 in 4 languages and held by 229 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
Tagung über Funktionalanalytische Methoden in der Numerischen Mathematik(
Book
)
28 editions published between 1967 and 2014 in 3 languages and held by 229 WorldCat member libraries worldwide
28 editions published between 1967 and 2014 in 3 languages and held by 229 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
)
26 editions published in 1968 in 3 languages and held by 223 WorldCat member libraries worldwide
26 editions published in 1968 in 3 languages and held by 223 WorldCat member libraries worldwide
Numerische Methoden der Approximationstheorie, Band 3 : Vortragsauszüge der Tagung über Numerische Methoden der Approximationstheorie,
vom 25. bis 31. Mai 1975 im Mathematischen Forschungsinstitut Oberwolfach (Schwarzwald) by
L Collatz(
Book
)
76 editions published between 1972 and 1984 in 3 languages and held by 218 WorldCat member libraries worldwide
76 editions published between 1972 and 1984 in 3 languages and held by 218 WorldCat member libraries worldwide
Numerische Behandlung von Differentialgleichungen by
L Collatz(
Book
)
13 editions published in 1951 in German and held by 205 WorldCat member libraries worldwide
13 editions published in 1951 in German and held by 205 WorldCat member libraries worldwide
Iterationsverfahren, Numerische Mathematik, Approximationstheorie by
L Collatz(
Book
)
32 editions published between 1970 and 1979 in 4 languages and held by 204 WorldCat member libraries worldwide
32 editions published between 1970 and 1979 in 4 languages and held by 204 WorldCat member libraries worldwide
Numerical treatment of free boundary value problems by
J Albrecht(
Book
)
13 editions published between 1981 and 1982 in 3 languages and held by 194 WorldCat member libraries worldwide
13 editions published between 1981 and 1982 in 3 languages and held by 194 WorldCat member libraries worldwide
Numerische Methoden der Approximationstheorie(
Book
)
in German and held by 187 WorldCat member libraries worldwide
in German and held by 187 WorldCat member libraries worldwide
more
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Audience Level
0 

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Kids  General  Special 
Related Identities
 Wetterling, Wolfgang W. E. 1932 Editor
 Meinardus, Günther 1926 Editor
 Mathematisches Forschungsinstitut Oberwolfach Editor
 Albrecht, J. (Julius) 1926 Author Editor
 Albrecht, J. (Julius) 1926 Author 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
Useful Links
Associated Subjects
Approximation theory Boundary value problems Boundary value problemsNumerical solutions Collatz, L.(Lothar), Combinatorial analysis Differential equations Differential equations, PartialNumerical solutions Differential equationsNumerical solutions Eigenvalues Functional analysis Game theory Germany Graph theory Integral equationsNumerical solutions Iterative methods (Mathematics) Mathematical optimization Mathematical physics Mathematicians Mathematics Nonlinear boundary value problems Nonlinear boundary value problemsNumerical solutions Nonlinear oscillations Numerical analysis Numerical calculations Programming (Mathematics)
Alternative Names
Collatz, L.
Collatz, L. 19101990
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 Duits wiskundige
Lothar Collatz German mathematician
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.
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コラッツ, L.
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