Claude Brezinski's Books

Extrapolation and Rational Approximation

The Works of the Main Contributors

By: Claude Brezinski,Michela Redivo-Zaglia

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Extrapolation and Rational Approximation

The Works of the Main Contributors

By: Claude Brezinski,Michela Redivo-Zaglia

This book paints a fresco of the field of extrapolation and rational approximation over the last several centuries to the present through the works of their primary contributors. It can serve as an introduction to the topics covered, including extrapolation methods, Padé approximation, orthogonal polynomials, continued fractions, Lanczos-type methods etc.; it also provides in depth discussion of the many links between these subjects. A highlight of this book is the presentation of the human side of the fields discussed via personal testimonies from contemporary researchers, their anecdotes, and their exclusive remembrances of some of the “actors.” This book shows how research in this domain started and evolved. Biographies of other scholars encountered have also been included. An important branch of mathematics is described in its historical context, opening the way to new developments. After a mathematical introduction, the book contains a precise description of the mathematical landscape of these fields spanning from the 19th century to the first part of the 20th. After an analysis of the works produced after that period (in particular those of Richardson, Aitken, Shanks, Wynn, and others), the most recent developments and applications are reviewed.

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Page Count

410

Publisher

Springer Nature

Published Date

ISBN 10

3030584186

ISBN 13

9783030584184

Biorthogonality and its Applications to Numerical Analysis

By: Claude Brezinski

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Biorthogonality and its Applications to Numerical Analysis

By: Claude Brezinski

This book explores the use of the concept of biorthogonality and discusses the various recurrence relations for the generalizations of the method of moments, the method of Lanczos, and the biconjugate gradient method. It is helpful for researchers in numerical analysis and approximation theory.

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Page Count

181

Publisher

CRC Press

Published Date

ISBN 10

1000104737

ISBN 13

9781000104738

Computational Aspects of Linear Control

By: Claude Brezinski

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Computational Aspects of Linear Control

By: Claude Brezinski

Many devices (we say dynamical systems or simply systems) behave like black boxes: they receive an input, this input is transformed following some laws (usually a differential equation) and an output is observed. The problem is to regulate the input in order to control the output, that is for obtaining a desired output. Such a mechanism, where the input is modified according to the output measured, is called feedback. The study and design of such automatic processes is called control theory. As we will see, the term system embraces any device and control theory has a wide variety of applications in the real world. Control theory is an interdisci plinary domain at the junction of differential and difference equations, system theory and statistics. Moreover, the solution of a control problem involves many topics of numerical analysis and leads to many interesting computational problems: linear algebra (QR, SVD, projections, Schur complement, structured matrices, localization of eigenvalues, computation of the rank, Jordan normal form, Sylvester and other equations, systems of linear equations, regulariza tion, etc), root localization for polynomials, inversion of the Laplace transform, computation of the matrix exponential, approximation theory (orthogonal poly nomials, Pad6 approximation, continued fractions and linear fractional transfor mations), optimization, least squares, dynamic programming, etc. So, control theory is also a. good excuse for presenting various (sometimes unrelated) issues of numerical analysis and the procedures for their solution. This book is not a book on control.

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Page Count

296

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461302617

ISBN 13

9781461302612

A Journey through the History of Numerical Linear Algebra

By: Claude Brezinski ,Gérard Meurant ,Michela Redivo-Zaglia

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A Journey through the History of Numerical Linear Algebra

By: Claude Brezinski ,Gérard Meurant ,Michela Redivo-Zaglia

This expansive volume describes the history of numerical methods proposed for solving linear algebra problems, from antiquity to the present day. The authors focus on methods for linear systems of equations and eigenvalue problems and describe the interplay between numerical methods and the computing tools available at the time. The second part of the book consists of 78 biographies of important contributors to the field. A Journey through the History of Numerical Linear Algebra will be of special interest to applied mathematicians, especially researchers in numerical linear algebra, people involved in scientific computing, and historians of mathematics.

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Page Count

813

Publisher

SIAM

Published Date

ISBN 10

1611977231

ISBN 13

9781611977233

History of Continued Fractions and Padé Approximants

By: Claude Brezinski

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History of Continued Fractions and Padé Approximants

By: Claude Brezinski

The history of continued fractions is certainly one of the longest among those of mathematical concepts, since it begins with Euclid's algorithm for the great est common divisor at least three centuries B.C. As it is often the case and like Monsieur Jourdain in Moliere's "Ie bourgeois gentilhomme" (who was speak ing in prose though he did not know he was doing so), continued fractions were used for many centuries before their real discovery. The history of continued fractions and Pade approximants is also quite im portant, since they played a leading role in the development of some branches of mathematics. For example, they were the basis for the proof of the tran scendence of 11' in 1882, an open problem for more than two thousand years, and also for our modern spectral theory of operators. Actually they still are of great interest in many fields of pure and applied mathematics and in numerical analysis, where they provide computer approximations to special functions and are connected to some convergence acceleration methods. Con tinued fractions are also used in number theory, computer science, automata, electronics, etc ...

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Page Count

556

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642581692

ISBN 13

9783642581694

Walter Gautschi, Volume 2

Selected Works with Commentaries

By: Claude Brezinski,Ahmed Sameh

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Walter Gautschi, Volume 2

Selected Works with Commentaries

By: Claude Brezinski,Ahmed Sameh

Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi’s most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter’s prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical Conditioning Special Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other Quadratures Gauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and Biography Miscellanea Works of Werner Gautschi

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Publisher

Birkhäuser

Published Date

ISBN 10

146147048X

ISBN 13

9781461470489

André-Louis Cholesky

Mathematician, Topographer and Army Officer

By: Claude Brezinski,Dominique Tournès

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André-Louis Cholesky

Mathematician, Topographer and Army Officer

By: Claude Brezinski,Dominique Tournès

This book traces the life of Cholesky (1875-1918), and gives his family history. After an introduction to topography, an English translation of an unpublished paper by him where he explained his method for linear systems is given, studied and replaced in its historical context. His other works, including two books, are also described as well as his involvement in teaching at a superior school by correspondence. The story of this school and its founder, Léon Eyrolles, are addressed. Then, an important unpublished book of Cholesky on graphical calculation is analyzed in detail and compared to similar contemporary publications. The biography of Ernest Benoit, who wrote the first paper where Cholesky ́s method is explained, is provided. Various documents, highlighting the life and the personality of Cholesky, end the book.

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Page Count

340

Publisher

Springer

Published Date

ISBN 10

3319081357

ISBN 13

9783319081359

History of Continued Fractions and Padé Approximants

By: Claude Brezinski

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History of Continued Fractions and Padé Approximants

By: Claude Brezinski

The concept of continued fractions os one of the oldest in the history of mathematics. It can be traced back to Euclid's algorithm for the greatest common divisor or even earlier. Continued fractions and Pade approximants played an important role in the development of many branches of mathematics, such as the spectral theory of operators, and in the solution of famous problems, such as the quadrature of the circle.

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Page Count

551

Publisher

Springer Verlag

Published Date

ISBN 10

0387152865

ISBN 13

9780387152868

Les Images de la Terre - Cosmographie, Geodesie, Topographie

By: Claude Brezinski

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Les Images de la Terre - Cosmographie, Geodesie, Topographie

By: Claude Brezinski

De tout temps l'Homme s'est déplacé sur Terre. Il lui a rapidement fallu trouver des repères ; le ciel en fournit. Il fallait alors comprendre pourquoi les astres revenaient périodiquement à la même place. La cosmographie était née. Quand il comprit que la Terre était une sphère, il fallut la mesurer : ce fut la géodésie. Puis la trianguler pour obtenir des distances et des angles, évaluer les hauteurs pour comprendre le relief. Enfin, la cartographie était née. C'est cette grande aventure de l'humanité que fait partager ce livre."--Résumé de l'éditeur.

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Page Count

300

Published Date

ISBN 10

2336277867

ISBN 13

9782336277868

Book's by Claude Brezinski

Extrapolation and Rational Approximation

Extrapolation and Rational Approximation

Biorthogonality and its Applications to Numerical Analysis

Biorthogonality and its Applications to Numerical Analysis

Computational Aspects of Linear Control

Computational Aspects of Linear Control

A Journey through the History of Numerical Linear Algebra

A Journey through the History of Numerical Linear Algebra

History of Continued Fractions and Padé Approximants

History of Continued Fractions and Padé Approximants

Walter Gautschi, Volume 2

Walter Gautschi, Volume 2

André-Louis Cholesky

André-Louis Cholesky

History of Continued Fractions and Padé Approximants

History of Continued Fractions and Padé Approximants

Les Images de la Terre - Cosmographie, Geodesie, Topographie

Les Images de la Terre - Cosmographie, Geodesie, Topographie

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