books in numerical linear algebra

[Omar_Absi]

Numerical Linear Algebra
By Lloyd N. Trefethen, David Bau III

• Publisher: SIAM: Society for Industrial and Applied Mathematics
• Number Of Pages: 373
• Publication Date: 1997-06-01
• ISBN-10 / ASIN: 0898713617
• ISBN-13 / EAN: 9780898713619
• Binding: Paperback

Product Description:

This is a concise, insightful introduction to the field of numerical linear algebra. The clarity and eloquence of the presentation make it popular with teachers and students alike. The text aims to expand the reader's view of the field and to present standard material in a novel way. All of the most important topics in the field are covered with a fresh perspective, including iterative methods for systems of equations and eigenvalue problems and the underlying principles of conditioning and stability. Presentation is in the form of 40 lectures, which each focus on one or two central ideas. The unity between topics is emphasized throughout, with no risk of getting lost in details and technicalities. The book breaks with tradition by beginning with the QR factorization - an important and fresh idea for students, and the thread that connects most of the algorithms of numerical linear algebra.​

Contents:

Preface; Acknowledgments; Part I: Fundamentals. Lecture 1: Matrix-Vector Multiplication; Lecture 2: Orthogonal Vectors and Matrices; Lecture 3: Norms; Lecture 4: The Singular Value Decomposition; Lecture 5: More on the SVD; Part II: QR Factorization and Least Squares. Lecture 6: Projectors; Lecture 7: QR Factorization; Lecture 8: Gram-Schmidt Orthogonalization; Lecture 9: MATLAB; Lecture 10: Householder Triangularization; Lecture 11: Least Squares Problems; Part III: Conditioning and Stability. Lecture 12: Conditioning and Condition Numbers; Lecture 13: Floating Point Arithmetic; Lecture 14: Stability; Lecture 15: More on Stability; Lecture 16: Stability of Householder Triangularization; Lecture 17: Stability of Back Substitution; Lecture 18: Conditioning of Least Squares Problems; Lecture 19: Stability of Least Squares Algorithms; Part IV: Systems of Equations. Lecture 20: Gaussian Elimination; Lecture 21: Pivoting; Lecture 22: Stability of Gaussian Elimination; Lecture 23: Cholesky Factorization; Part V: Eigenvalues. Lecture 24: Eigenvalue Problems; Lecture 25: Overview of Eigenvalue Algorithms; Lecture 26: Reduction to Hessenberg or Tridiagonal Form; Lecture 27: Rayleigh Quotient, Inverse Iteration; Lecture 28: QR Algorithm without Shifts; Lecture 29: QR Algorithm with Shifts; Lecture 30: Other Eigenvalue Algorithms; Lecture 31: Computing the SVD; Part VI: Iterative Methods. Lecture 32: Overview of Iterative Methods; Lecture 33: The Arnoldi Iteration; Lecture 34: How Arnoldi Locates Eigenvalues; Lecture 35: GMRES; Lecture 36: The Lanczos Iteration; Lecture 37: From Lanczos to Gauss Quadrature; Lecture 38: Conjugate Gradients; Lecture 39: Biorthogonalization Methods; Lecture 40: Preconditioning; Appendix: The Definition of Numerical Analysis; Notes; Bibliography; Index.​

Audience:

Written on the graduate or advanced undergraduate level, this book can be used widely for teaching. Professors looking for an elegant presentation of the topic will find it an excellent teaching tool for a one-semester graduate or advanced undergraduate course. A major contribution to the applied mathematics literature, most researchers in the field will consider it a necessary addition to their personal collections.​

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[Omar_Absi]

Numerical Linear Algebra
(Texts in Applied Mathematics)
By Grégoire Allaire, Sidi Mahmoud Kaber

• Publisher: Springer
• Number Of Pages: 276
• Publication Date: 2007-12-05
• ISBN-10 / ASIN: 0387341595
• ISBN-13 / EAN: 9780387341590
• Binding: Hardcover

Product Description:

This book brings together linear algebra, numerical methods and an easy to use programming environment under Matlab (and Scilab). One of the key features of the book is the worked out examples and exercises at the end of each chapter. The reader is asked to do some numerical experiments in Matlab and then to prove the results theoretically.

The book is a combination and update of two earlier French books by the authors. It is appropriate for both undergraduate and beginning graduate courses in mathematics as well as for working scientists and engineers as a self-study tool and reference.​

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[Omar_Absi]

Applied Numerical Linear Algebra
By James W. Demmel

• Publisher: SIAM
• Number Of Pages: 431
• Publication Date: 1997-08-01
• ISBN-10 / ASIN: 0898713897
• ISBN-13 / EAN: 9780898713893
• Binding: Paperback

Product Description:

Designed for use by first-year graduate students from a variety of engineering and scientific disciplines, this comprehensive textbook covers the solution of linear systems, least squares problems, eigenvalue problems, and the singular value decomposition. The author, who helped design the widely used LAPACK and ScaLAPACK linear algebra libraries, draws on this experience to present state-of-the-art techniques for these problems, including recommendations of which algorithms to use in a variety of practical situations.
If you are looking for a textbook that - teaches state-of-the-art techniques for solving linear algebra problems, - covers the most important methods for dense and sparse problems, - presents both the mathematical background and good software techniques, - is self-contained, assuming only a good undergraduate background in linear algebra,
then this is the book for you.
Algorithms are derived in a mathematically illuminating way, including condition numbers and error bounds. Direct and iterative algorithms, suitable for dense and sparse matrices, are discussed. Algorithm design for modern computer architectures, where moving data is often more expensive than arithmetic operations, is discussed in detail, using LAPACK as an illustration. There are many numerical examples throughout the text and in the problems at the ends of chapters, most of which are written in Matlab and are freely available on the Web.
Material either not available elsewhere, or presented quite differently in other textbooks, includes - a discussion of the impact of modern cache-based computer memories on algorithm design; - frequent recommendations and pointers in the text to the best software currently available, including a detailed performance comparison of state-of-the-art software for eigenvalue and least squares problems, and a description of sparse direct solvers for serial and parallel machines; - a discussion of iterative methods ranging from Jacobi's method to multigrid and domain decomposition, with performance comparisons on a model problem; - a great deal of Matlab-based software, available on the Web, which either implements algorithms presented in the book, produces the figures in the book, or is used in homework problems; - numerical examples drawn from fields ranging from mechanical vibrations to computational geometry; - high-accuracy algorithms for solving linear systems and eigenvalue problems, along with tighter "relative" error bounds; - dynamical systems interpretations of some eigenvalue algorithms.
Demmel discusses several current research topics, making students aware of both the lively research taking place and connections to other parts of numerical analysis, mathematics, and computer science. Some of this material is developed in questions at the end of each chapter, which are marked Easy, Medium, or Hard according to their difficulty. Some questions are straightforward, supplying proofs of lemmas used in the text. Others are more difficult theoretical or computing problems. Questions involving significant amounts of programming are marked Programming. The computing questions mainly involve Matlab programming, and others involve retrieving, using, and perhaps modifying LAPACK code from NETLIB.


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[Omar_Absi]

Numerical Linear Algebra on High-Performance Computers
(Software, Environments and Tools)
By Jack J. Dongarra, Iain S. Duff, Danny C. Sorensen, Hank A. van der Vorst

• Publisher: Society for Industrial Mathematics
• Number Of Pages: 360
• Publication Date: 1987-01-01
• ISBN-10 / ASIN: 0898714281
• ISBN-13 / EAN: 9780898714289
• Binding: Paperback

Product Description:

This book presents a unified treatment of recently developed techniques and current understanding about solving systems of linear equations and large scale eigenvalue problems on high-performance computers. It provides a rapid introduction to the world of vector and parallel processing for these linear algebra applications. Topics include major elements of advanced-architecture computers and their performance, recent algorithmic development, and software for direct solution of dense matrix problems, direct solution of sparse systems of equations, iterative solution of sparse systems of equations, and solution of large sparse eigenvalue problems. This book supercedes the SIAM publication Solving Linear Systems on Vector and Shared Memory Computers, which appeared in 1990. The new book includes a considerable amount of new material in addition to incorporating a substantial revision of existing text.



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[Omar_Absi]

Linear Algebra and Its Applications
By Gilbert Strang

• Publisher: Brooks Cole
• Number Of Pages: 520
• Publication Date: 1988-02-10
• ISBN-10 / ASIN: 0155510053
• ISBN-13 / EAN: 9780155510050
• Binding: Hardcover

Product Description:

With a highly applied and computational focus, this book combines the important underlying theory with examples from electrical engineering, computer science, physics, biology and economics. An expanded list of computer codes in an appendix and more computer-solvable exercises in the text reflect Strang?s interest in computational linear algebra. Many exercises appear in the sections and in the chapter reviews. Exercises are simple but instructive.​

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[Omar_Absi]

Matrix Algorithms Volume I: Basic Decompositions
by G. W. Stewart

• Publisher: SIAM: Society for Industrial and Applied Mathematics
• Number Of Pages: 478
• Publication Date: 1998-08-01
• ISBN-10 / ASIN: 0898714141
• ISBN-13 / EAN: 9780898714142
• Binding: Paperback

Product Description:

This thorough, concise, and superbly written volume is the first in a self-contained five-volume series devoted to matrix algorithms. It focuses on the computation of matrix decompositions - the factorization of matrices into products of similar ones. The first two chapters provide the required background from mathematics and computer science needed to work effectively in matrix computations. The remaining chapters are devoted to the computation and applications of the LU and QR decompositions. The series is aimed at the nonspecialist who needs more than black-box proficiency with matrix computations. A certain knowledge of elementary analysis and linear algebra is assumed, as well as a reasonable amount of programming experience. The guiding principle, that if something is worth explaining, it is worth explaining fully, has necessarily restricted the scope of the series, but the selection of topics should give the reader a sound basis for further study.​

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Matrix Algorithms, Volume II: Eigensystems
By G. W. Stewart

• Publisher: SIAM: Society for Industrial and Applied Mathematics
• Number Of Pages: 469
• Publication Date: 2001-08-01
• ISBN-10 / ASIN: 0898715032
• ISBN-13 / EAN: 9780898715033
• Binding: Paperback

Product Description:

This is the second volume in a projected five-volume survey of numerical linear algebra and matrix algorithms. It treats the numerical solution of dense and large-scale eigenvalue problems with an emphasis on algorithms and the theoretical background required to understand them. The notes and reference sections contain pointers to other methods along with historical comments. The book is divided into two parts: dense eigenproblems and large eigenproblems. The first part gives a full treatment of the widely used QR algorithm, which is then applied to the solution of generalized eigenproblems and the computation of the singular value decomposition. The second part treats Krylov sequence methods such as the Lanczos and Arnoldi algorithms and presents a new treatment of the Jacobi-Davidson method. These volumes are not intended to be encyclopedic, but provide the reader with the theoretical and practical background to read the research literature and implement or modify new algorithms.​

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[Omar_Absi]

Numerical Polynomial Algebra
By Hans J. Stetter

• Publisher: SIAM: Society for Industrial and Applied Mathematics
• Number Of Pages: 488
• Publication Date: 2004-05-01
• ISBN-10 / ASIN: 0898715571
• ISBN-13 / EAN: 9780898715576
• Binding: Paperback

Product Description:

In many important areas of scientific computing, polynomials in one or more variables are employed in the mathematical modeling of real-life phenomena; yet most of classical computer algebra assumes exact rational data. This book is the first comprehensive treatment of numerical polynomial algebra, an emerging area that falls between classical numerical analysis and classical computer algebra, and which has received surprisingly little attention so far. The author introduces a conceptual framework that permits the meaningful solution of various algebraic problems with multivariate polynomial equations whose coefficients have some indeterminacy; for this purpose, he combines approaches of both numerical linear algebra and commutative algebra. For the application scientist, this book provides both a survey of polynomial problems in scientific computing that may be solved numerically and a guide to their numerical treatment. In addition, the book provides both introductory sections and novel extensions, making it more easily accessible.​

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[ابو رشاد]

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[Omar_Absi]

Re: رد : books in numerical linear algebra

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شكراً لك أخي العزي أبو رشاد على كلماتك الرقيقة

أخي العزيز
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[farahramzi]

شكراً لك

 

[Wakko]

Hi Omar_Absi.....!
Thankx for all.