A Journey Through The History Of Numerical Linear Algebra
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A Journey Through The History Of Numerical Linear Algebra
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Author : Claude Brezinski
language : en
Publisher: SIAM
Release Date : 2022-12-06
A Journey Through The History Of Numerical Linear Algebra written by Claude Brezinski and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-06 with Mathematics categories.
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.
Numerical Linear Algebra
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Author : William Layton
language : en
Publisher: World Scientific
Release Date : 2020-07-14
Numerical Linear Algebra written by William Layton and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-14 with Mathematics categories.
'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.
An Introduction To Numerical Linear Algebra
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Author : Leslie Fox
language : en
Publisher: Oxford University Press, USA
Release Date : 1965
An Introduction To Numerical Linear Algebra written by Leslie Fox and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Language Arts & Disciplines categories.
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.
Numerical Linear Algebra Theory And Applications
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Author : Larisa Beilina
language : en
Publisher: Springer
Release Date : 2017-09-19
Numerical Linear Algebra Theory And Applications written by Larisa Beilina and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-19 with Mathematics categories.
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.
Numerical Linear Algebra And Matrix Factorizations
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Author : Tom Lyche
language : en
Publisher: Springer Nature
Release Date : 2020-03-02
Numerical Linear Algebra And Matrix Factorizations written by Tom Lyche and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-02 with Mathematics categories.
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.
Numerical Linear Algebra
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Author : V. SUNDARAPANDIAN
language : en
Publisher: PHI Learning Pvt. Ltd.
Release Date : 2008-04-23
Numerical Linear Algebra written by V. SUNDARAPANDIAN and has been published by PHI Learning Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-23 with Mathematics categories.
This well-organized text provides a clear analysis of the fundamental concepts of numerical linear algebra. It presents various numerical methods for the basic topics of linear algebra with a detailed discussion on theory, algorithms, and MATLAB implementation. The book provides a review of matrix algebra and its important results in the opening chapter and examines these results in the subsequent chapters. With clear explanations, the book analyzes different kinds of numerical algorithms for solving linear algebra such as the elimination and iterative methods for linear systems, the condition number of a matrix, singular value decomposition (SVD) of a matrix, and linear least-squares problem. In addition, it describes the Householder and Givens matrices and their applications, and the basic numerical methods for solving the matrix eigenvalue problem. Finally, the text reviews the numerical methods for systems and control. Key Features Includes numerous worked-out examples to help students grasp the concepts easily. Provides chapter-end exercises to enable students to check their comprehension of the topics discussed. Gives answers to exercises with hints at the end of the book. Uses MATLAB software for problem-solving. Primarily designed as a textbook for postgraduate students of Mathematics, this book would also serve as a handbook on matrix computations for scientists and engineers.
Numerical Linear Algebra
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Author : Holger Wendland
language : en
Publisher: Cambridge University Press
Release Date : 2017-11-16
Numerical Linear Algebra written by Holger Wendland and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-16 with Computers categories.
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.
Numerical Linear Algebra
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Author : Lloyd N. Trefethen
language : en
Publisher: SIAM
Release Date : 1997-06-01
Numerical Linear Algebra written by Lloyd N. Trefethen and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-01 with Mathematics categories.
Numerical Linear Algebra is a concise, insightful, and elegant introduction to the field of numerical linear algebra.
Applied Numerical Linear Algebra
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Author : James W. Demmel
language : en
Publisher: SIAM
Release Date : 1997-08-01
Applied Numerical Linear Algebra written by James W. Demmel and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-01 with Mathematics categories.
This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.
Error Norm Estimation In The Conjugate Gradient Algorithm
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Author : Gérard Meurant
language : en
Publisher: SIAM
Release Date : 2024-01-30
Error Norm Estimation In The Conjugate Gradient Algorithm written by Gérard Meurant and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-30 with Mathematics categories.
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.