A Journey Through The History Of Numerical Linear Algebra

Author : Claude Brezinski ,Gérard Meurant ,Michela Redivo-Zaglia
Publisher : SIAM
Page : 813 pages
File Size : 49,8 Mb
Release : 2022-12-06
Category : Mathematics
ISBN : 9781611977233

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A Journey through the History of Numerical Linear Algebra by Claude Brezinski ,Gérard Meurant ,Michela Redivo-Zaglia Pdf

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.

Author : James W. Demmel
Publisher : SIAM
Page : 426 pages
File Size : 46,5 Mb
Release : 1997-08-01
Category : Mathematics
ISBN : 9780898713893

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Applied Numerical Linear Algebra by James W. Demmel Pdf

This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.

Author : Gérard Meurant ,Petr Tichý
Publisher : SIAM
Page : 138 pages
File Size : 48,7 Mb
Release : 2024-01-30
Category : Mathematics
ISBN : 9781611977868

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Error Norm Estimation in the Conjugate Gradient Algorithm by Gérard Meurant ,Petr Tichý Pdf

The conjugate gradient (CG) algorithm is almost always the iterative method of choice for solving linear systems with symmetric positive definite matrices. This book describes and analyzes techniques based on Gauss quadrature rules to cheaply compute bounds on norms of the error. The techniques can be used to derive reliable stopping criteria. How to compute estimates of the smallest and largest eigenvalues during CG iterations is also shown. The algorithms are illustrated by many numerical experiments, and they can be easily incorporated into existing CG codes. The book is intended for those in academia and industry who use the conjugate gradient algorithm, including the many branches of science and engineering in which symmetric linear systems have to be solved.

Author : Larisa Beilina,Evgenii Karchevskii,Mikhail Karchevskii
Publisher : Springer
Page : 450 pages
File Size : 44,6 Mb
Release : 2017-09-19
Category : Mathematics
ISBN : 9783319573045

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Numerical Linear Algebra: Theory and Applications by Larisa Beilina,Evgenii Karchevskii,Mikhail Karchevskii Pdf

This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigenproblems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.

Author : Tom Lyche
Publisher : Springer Nature
Page : 376 pages
File Size : 50,9 Mb
Release : 2020-03-02
Category : Mathematics
ISBN : 9783030364687

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Numerical Linear Algebra and Matrix Factorizations by Tom Lyche Pdf

After reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them. Since these problems can be large and difficult to handle, much can be gained by understanding and taking advantage of special structures. This in turn requires a good grasp of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra, because it allows us to tackle complex problems by solving a sequence of easier ones. The main characteristics of this book are as follows: It is self-contained, only assuming that readers have completed first-year calculus and an introductory course on linear algebra, and that they have some experience with solving mathematical problems on a computer. The book provides detailed proofs of virtually all results. Further, its respective parts can be used independently, making it suitable for self-study. The book consists of 15 chapters, divided into five thematically oriented parts. The chapters are designed for a one-week-per-chapter, one-semester course. To facilitate self-study, an introductory chapter includes a brief review of linear algebra.

Author : William Layton,Myron Mike Sussman
Publisher : World Scientific
Page : 274 pages
File Size : 43,6 Mb
Release : 2020-07-14
Category : Mathematics
ISBN : 9789811223914

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Numerical Linear Algebra by William Layton,Myron Mike Sussman Pdf

'The numerical algorithms presented are written in pseudocode and based on MATLAB, a programming and numeric computing platform widely used in STEM fields. Thus, no formal training in computer science or knowledge of any specific programming language is needed to parse the algorithms. Summing up: Recommended.'CHOICEMany students come to numerical linear algebra from science and engineering seeking modern tools and an understanding of how the tools work and their limitations. Often their backgrounds and experience are extensive in applications of numerical methods but limited in abstract mathematics and matrix theory. Often enough it is limited to multivariable calculus, basic differential equations and methods of applied mathematics. This book introduces modern tools of numerical linear algebra based on this background, heavy in applied analysis but light in matrix canonical forms and their algebraic properties. Each topic is presented as algorithmic ideas and through a foundation based on mostly applied analysis. By picking a path through the book appropriate for the level, it has been used for both senior level undergraduates and beginning graduate classes with students from diverse fields and backgrounds.

Author : Leslie Fox
Publisher : Unknown
Page : 0 pages
File Size : 53,9 Mb
Release : 1964
Category : Algebra
ISBN : 0198534078

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An Introduction to Numerical Linear Algebra by Leslie Fox Pdf

Author : Charles G. Cullen
Publisher : Pws Publishing Company
Page : 314 pages
File Size : 55,6 Mb
Release : 1994
Category : Mathematics
ISBN : 0534936903

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An Introduction to Numerical Linear Algebra by Charles G. Cullen Pdf

This text aims to combine the seemingly disparate subject areas of linear algebra and numerics under one cover. It comes with software MATALG (IBM 3.5 disk), packaged specifically by the author. Other computer algebra systems (CAS) such as MATLAB or Mathematica are also compatible with this book.

Author : Lloyd N. Trefethen,David Bau
Publisher : SIAM
Page : 387 pages
File Size : 40,7 Mb
Release : 2022-06-17
Category : Mathematics
ISBN : 9781611977165

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Numerical Linear Algebra by Lloyd N. Trefethen,David Bau Pdf

Since its original appearance in 1997, Numerical Linear Algebra has been a leading textbook in its field, used in universities around the world. It is noted for its 40 lecture-sized short chapters and its clear and inviting style. It is reissued here with a new foreword by James Nagy and a new afterword by Yuji Nakatsukasa about subsequent developments.

Author : Holger Wendland
Publisher : Cambridge University Press
Page : 419 pages
File Size : 53,8 Mb
Release : 2017-11-16
Category : Computers
ISBN : 9781107147133

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Numerical Linear Algebra by Holger Wendland Pdf

This self-contained introduction to numerical linear algebra provides a comprehensive, yet concise, overview of the subject. It includes standard material such as direct methods for solving linear systems and least-squares problems, error, stability and conditioning, basic iterative methods and the calculation of eigenvalues. Later chapters cover more advanced material, such as Krylov subspace methods, multigrid methods, domain decomposition methods, multipole expansions, hierarchical matrices and compressed sensing. The book provides rigorous mathematical proofs throughout, and gives algorithms in general-purpose language-independent form. Requiring only a solid knowledge in linear algebra and basic analysis, this book will be useful for applied mathematicians, engineers, computer scientists, and all those interested in efficiently solving linear problems.

Author : Leslie Fox
Publisher : Oxford University Press, USA
Page : 354 pages
File Size : 51,6 Mb
Release : 1965
Category : Language Arts & Disciplines
ISBN : UOM:39015000962335

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An Introduction to Numerical Linear Algebra by Leslie Fox Pdf

Problems involving linear algebra arise in many contexts of scientific computation, either directly or through the replacement of continuous systems by discrete approximations. This introduction covers the practice of matrix algebra and manipulation, and the theory and practice of direct and iterative methods for solving linear simultaneous algebraic equations, inverting matrices, and determining the latent roots and vectors of matrices. Special attention is given to the important problem of error analysis and numerous examples illustrate the procedures recommended in various circumstances. The emphasis is on the reasons for selecting particular numerical methods rather than on programming or coding.

Author : Ricardo V Teixeira,Jang-woo Park
Publisher : World Scientific
Page : 406 pages
File Size : 49,9 Mb
Release : 2020-05-29
Category : Mathematics
ISBN : 9789811214523

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Mathemagics: A Magical Journey Through Advanced Mathematics - Connecting More Than 60 Magic Tricks To High-level Math by Ricardo V Teixeira,Jang-woo Park Pdf

'This delightful book connects mathematical concepts in a dozen areas to magic tricks. Expositions of the mathematics precede description and analysis of the tricks. The expositions are too short for in-depth learning; the intent is to give sophomores a taste of the content and ideas of later mathematics courses. Each chapter features exercises on the mathematics, and students can have fun practicing the tricks.'Mathematics MagazineTeixeira and Park present over 60 different magic tricks while introducing students to high-level math areas. Readers will learn really interesting ideas that will better prepare them for future courses and help them finding areas they might want to study deeper. And as a 'side effect' students will learn amazing magic tricks, century-old secrets, and details from famous magicians and mathematicians.The material was written to quickly present key concepts in several mathematical areas in direct way. Little or no proficiency in math is assumed. In fact, students do not require any Calculus knowledge. And since chapters are almost independent from each other, this book also work as introduction to several other courses.Topics covered include mathematical proofs, probability, abstract algebra, linear algebra, mathematical computing, number theory, coding theory, geometry, topology, real analysis, numerical analysis and history of math.

Author : Philippe G. Ciarlet
Publisher : Cambridge University Press
Page : 452 pages
File Size : 54,6 Mb
Release : 1989-08-31
Category : Computers
ISBN : 0521327881

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Introduction to Numerical Linear Algebra and Optimisation by Philippe G. Ciarlet Pdf

Based on courses taught to advanced undergraduate students, this book offers a broad introduction to the methods of numerical linear algebra and optimization. The prerequisites are familiarity with the basic properties of matrices, finite-dimensional vector spaces and advanced calculus, and some exposure to fundamental notions from functional analysis. The book is divided into two parts. The first part deals with numerical linear algebra (numerical analysis of matrices, direct and indirect methods for solving linear systems, calculation of eigenvalues and eigenvectors) and the second, optimizations (general algorithms, linear and nonlinear programming). Summaries of basic mathematics are provided, proof of theorems are complete yet kept as simple as possible, applications from physics and mechanics are discussed, a great many exercises are included, and there is a useful guide to further reading.

Author : Lloyd N. Trefethen,David Bau, III
Publisher : SIAM
Page : 356 pages
File Size : 46,9 Mb
Release : 1997-06-01
Category : Mathematics
ISBN : 9780898713619

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Numerical Linear Algebra by Lloyd N. Trefethen,David Bau, III Pdf

Numerical Linear Algebra is a concise, insightful, and elegant introduction to the field of numerical linear algebra.

Author : Eric Darve,Mary Wootters
Publisher : SIAM
Page : 420 pages
File Size : 46,6 Mb
Release : 2021-09-02
Category : Mathematics
ISBN : 9781611976557

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Numerical Linear Algebra with Julia by Eric Darve,Mary Wootters Pdf

Numerical Linear Algebra with Julia provides in-depth coverage of fundamental topics in numerical linear algebra, including how to solve dense and sparse linear systems, compute QR factorizations, compute the eigendecomposition of a matrix, and solve linear systems using iterative methods such as conjugate gradient. Julia code is provided to illustrate concepts and allow readers to explore methods on their own. Written in a friendly and approachable style, the book contains detailed descriptions of algorithms along with illustrations and graphics that emphasize core concepts and demonstrate the algorithms. Numerical Linear Algebra with Julia is a textbook for advanced undergraduate and graduate students in most STEM fields and is appropriate for courses in numerical linear algebra. It may also serve as a reference for researchers in various fields who depend on numerical solvers in linear algebra.