Numerical Linear Algebra Theory And Applications

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Numerical Linear Algebra Theory And Applications

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Author : Larisa Beilina
language : en
Publisher: Springer
Release Date : 2018-01-22

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 2018-01-22 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.

Matrix Algebra

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Author : James E. Gentle
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-06

Matrix Algebra written by James E. Gentle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-06 with Mathematics categories.

Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. The first part of this book presents the relevant aspects of the theory of matrix algebra for applications in statistics. This part begins with the fundamental concepts of vectors and vector spaces, next covers the basic algebraic properties of matrices, then describes the analytic properties of vectors and matrices in the multivariate calculus, and finally discusses operations on matrices in solutions of linear systems and in eigenanalysis. This part is essentially self-contained. The second part of the book begins with a consideration of various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. The second part also describes some of the many applications of matrix theory in statistics, including linear models, multivariate analysis, and stochastic processes. The brief coverage in this part illustrates the matrix theory developed in the first part of the book. The first two parts of the book can be used as the text for a course in matrix algebra for statistics students, or as a supplementary text for various courses in linear models or multivariate statistics. The third part of this book covers numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Although the book is not tied to any particular software system, it describes and gives examples of the use of modern computer software for numerical linear algebra. This part is essentially self-contained, although it assumes some ability to program in Fortran or C and/or the ability to use R/S-Plus or Matlab. This part of the book can be used as the text for a course in statistical computing, or as a supplementary text for various courses that emphasize computations. The book includes a large number of exercises with some solutions provided in an appendix.

Numerical Linear Algebra In Signals Systems And Control

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Author : Paul Van Dooren
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-21

Numerical Linear Algebra In Signals Systems And Control written by Paul Van Dooren and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-21 with Technology & Engineering categories.

The purpose of Numerical Linear Algebra in Signals, Systems and Control is to present an interdisciplinary book, blending linear and numerical linear algebra with three major areas of electrical engineering: Signal and Image Processing, and Control Systems and Circuit Theory. Numerical Linear Algebra in Signals, Systems and Control will contain articles, both the state-of-the-art surveys and technical papers, on theory, computations, and applications addressing significant new developments in these areas. The goal of the volume is to provide authoritative and accessible accounts of the fast-paced developments in computational mathematics, scientific computing, and computational engineering methods, applications, and algorithms. The state-of-the-art surveys will benefit, in particular, beginning researchers, graduate students, and those contemplating to start a new direction of research in these areas. A more general goal is to foster effective communications and exchange of information between various scientific and engineering communities with mutual interests in concepts, computations, and workable, reliable practices.

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.

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 With Applications

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Author : William Ford
language : en
Publisher:
Release Date : 2014-09-02

Numerical Linear Algebra With Applications written by William Ford and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-02 with Computers categories.

Designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, Numerical Linear Algebra with Applications contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. It provides necessary mathematical background information for those who want to learn to solve linear algebra problems, and offers a thorough explanation of the issues and methods for practical computing, using MATLAB as the vehicle for computation. The proofs of required results are provided without leaving out critical details. The Preface suggests ways in which the book can be used with or without an intensive study of proofs. Six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra Detailed explanations and examples A through discussion of the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra Examples from engineering and science applications

Numerical Linear Algebra For Applications In Statistics

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Author : James E. Gentle
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Numerical Linear Algebra For Applications In Statistics written by James E. Gentle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Numerical linear algebra is one of the most important subjects in the field of statistical computing. Statistical methods in many areas of application require computations with vectors and matrices. This book describes accurate and efficient computer algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Although the book is not tied to any particular software system, it describes and gives examples of the use of modern computer software for numerical linear algebra. An understanding of numerical linear algebra requires basic knowledge both of linear algebra and of how numerical data are stored and manipulated in the computer. The book begins with a discussion of the basics of numerical computations, and then describes the relevant properties of matrix inverses, matrix factorizations, matrix and vector norms, and other topics in linear algebra; hence, the book is essentially self- contained. The topics addressed in this bookconstitute the most important material for an introductory course in statistical computing, and should be covered in every such course. The book includes exercises and can be used as a text for a first course in statistical computing or as supplementary text for various courses that emphasize computations. James Gentle is University Professor of Computational Statistics at George Mason University. During a thirteen-year hiatus from academic work before joining George Mason, he was director of research and design at the world's largest independent producer of Fortran and C general-purpose scientific software libraries. These libraries implement many algorithms for numerical linear algebra. He is a Fellow of the American Statistical Association and member of the International Statistical Institute. He has held several national

Guaranteed Accuracy In Numerical Linear Algebra

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Author : S.K. Godunov
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-06-30

Guaranteed Accuracy In Numerical Linear Algebra written by S.K. Godunov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-06-30 with Computers categories.

There exists a vast literature on numerical methods of linear algebra. In our bibliography list, which is by far not complete, we included some monographs on the subject [46], [15], [32], [39], [11], [21]. The present book is devoted to the theory of algorithms for a single problem of linear algebra, namely, for the problem of solving systems of linear equations with non-full-rank matrix of coefficients. The solution of this problem splits into many steps, the detailed discussion of which are interest ing problems on their own (bidiagonalization of matrices, computation of singular values and eigenvalues, procedures of deflation of singular values, etc. ). Moreover, the theory of algorithms for solutions of the symmetric eigenvalues problem is closely related to the theory of solv ing linear systems (Householder's algorithms of bidiagonalization and tridiagonalization, eigenvalues and singular values, etc. ). It should be stressed that in this book we discuss algorithms which to computer programs having the virtue that the accuracy of com lead putations is guaranteed. As far as the final program product is con cerned, this means that the user always finds an unambiguous solution of his problem. This solution might be of two kinds: 1. Solution of the problem with an estimate of errors, where abso lutely all errors of input data and machine round-offs are taken into account. 2.

Numerical Linear Algebra And Applications

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Author : Biswa Nath Datta
language : en
Publisher: SIAM
Release Date : 2010-01-01

Numerical Linear Algebra And Applications written by Biswa Nath Datta and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-01 with Mathematics categories.

Full of features and applications, this acclaimed textbook for upper undergraduate level and graduate level students includes all the major topics of computational linear algebra, including solution of a system of linear equations, least-squares solutions of linear systems, computation of eigenvalues, eigenvectors, and singular value problems. Drawing from numerous disciplines of science and engineering, the author covers a variety of motivating applications. When a physical problem is posed, the scientific and engineering significance of the solution is clearly stated. Each chapter contains a summary of the important concepts developed in that chapter, suggestions for further reading, and numerous exercises, both theoretical and MATLAB and MATCOM based. The author also provides a list of key words for quick reference. The MATLAB toolkit available online, 'MATCOM', contains implementations of the major algorithms in the book and will enable students to study different algorithms for the same problem, comparing efficiency, stability, and accuracy.

Matrices

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Author : Denis Serre
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-26

Matrices written by Denis Serre and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-26 with Mathematics categories.

In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. With forty percent new material, this second edition is significantly different from the first edition. Newly added topics include: • Dunford decomposition, • tensor and exterior calculus, polynomial identities, • regularity of eigenvalues for complex matrices, • functional calculus and the Dunford–Taylor formula, • numerical range, • Weyl's and von Neumann’s inequalities, and • Jacobi method with random choice. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the École Normale Supérieure de Lyon.