Numerical Linear Algebra and Applications

by Biswa Nath Datta

Author	: Biswa Nath Datta
Publisher	: SIAM
Total Pages	: 546
Release	: 2010-01-01
Genre	: Mathematics
ISBN	: 0898717655

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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.

Numerical Linear Algebra for Applications in Statistics

by James E. Gentle

Author	: James E. Gentle
Publisher	: Springer Science & Business Media
Total Pages	: 229
Release	: 2012-12-06
Genre	: Mathematics
ISBN	: 1461206235

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Accurate and efficient computer algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Regardless of the software system used, the book describes and gives examples of the use of modern computer software for numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes the relevant properties of matrix inverses, factorisations, matrix and vector norms, and other topics in linear algebra. The book is essentially self- contained, with the topics addressed constituting the essential material for an introductory course in statistical computing. Numerous exercises allow the text to be used for a first course in statistical computing or as supplementary text for various courses that emphasise computations.

Numerical Linear Algebra with Applications

by William Ford

Author	: William Ford
Publisher	: Academic Press
Total Pages	: 629
Release	: 2014-09-14
Genre	: Mathematics
ISBN	: 0123947847

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Numerical Linear Algebra with Applications is designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, using MATLAB as the vehicle for computation. The book 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. The text consists of six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra. It explains in great detail the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra. In addition to examples from engineering and science applications, 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. This book will be a useful reference for graduate or advanced undergraduate students in engineering, science, and mathematics. It will also appeal to professionals in engineering and science, such as practicing engineers who want to see how numerical linear algebra problems can be solved using a programming language such as MATLAB, MAPLE, or Mathematica. - 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

Applied Numerical Linear Algebra

by James W. Demmel

Author	: James W. Demmel
Publisher	: SIAM
Total Pages	: 426
Release	: 1997-08-01
Genre	: Mathematics
ISBN	: 0898713897

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

Numerical Linear Algebra: Theory and Applications

by Larisa Beilina

Author	: Larisa Beilina
Publisher	: Springer
Total Pages	: 459
Release	: 2017-09-19
Genre	: Mathematics
ISBN	: 3319573047

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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

by Holger Wendland

Author	: Holger Wendland
Publisher	: Cambridge University Press
Total Pages	: 419
Release	: 2018
Genre	: Computers
ISBN	: 1107147131

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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.

Introduction to Applied Linear Algebra

by Stephen Boyd

Author	: Stephen Boyd
Publisher	: Cambridge University Press
Total Pages	: 477
Release	: 2018-06-07
Genre	: Business & Economics
ISBN	: 1316518965

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A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Matrix Algebra

by James E. Gentle

Author	: James E. Gentle
Publisher	: Springer Science & Business Media
Total Pages	: 536
Release	: 2007-07-27
Genre	: Computers
ISBN	: 0387708723

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Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.

Numerical Linear Algebra and Matrix Factorizations

by Tom Lyche

Author	: Tom Lyche
Publisher	: Springer Nature
Total Pages	: 376
Release	: 2020-03-02
Genre	: Mathematics
ISBN	: 3030364682

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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.