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《应用数值线性代数》是2011年2月1日清华大学出版社出版的图书，作者是戴梅尔。本书不仅给出了数值线性代数的常用算法，而且也介绍了多重网格法和区域分解法等新算法，并指导读者如何编写数值软件以及从何处找到适用的优秀数值满府反祖随层绝十历软件。可作为计算数学和相关理工科专业一年级研究生的教材，也可作为从事科学计算只的广大科技工作者的参考书。
- 书名 应用数值线性代数
- 作者 (美国)戴梅尔(James W.Demmel)
- 原版名称 Applied Numerical Linear Algebra
- ISBN 9787302245001, 7302245002
- 页数 419页
作者简介
作者:(美国)戴梅尔(James W.Demmel)
James Demmel is a Profes围唱情sor in the Computer Science Division and Mathematics D来自epartment at the University of California, Berkeley.
内容简介
《应用数值线性360百科代数(影印版)》内晚道重味容简介:Designed for use by first-year graduate students from a variety of engineering and scientific disciplines, t立切his comprehensive textbook covers the solution 调任些of linear systems, least squares problems, eigenvalue pro稳水眼沉blems, and the singular value d权口环ecomposition. The author, who helped design the widely used LA参肉图望村输探球灯副川PACK and ScaLAP成剂知何着拉ACK linear 误钱algebra libraries, draws on this experience to present state-of-th略征她见e-art techni作批问元孙材投神ques for these problems, including recommendations of which algorithms to use in a variety of practical sit看伤增行甲抗席室防司uations.
媒体评论
部传载延住爱而机This book is a friendly treatment of numerical linear algebra tailored to first-year graduate students from a variety of engineering a来自nd scientific disciplines. The treatment of rounding er360百科ror analysis and perturbation theory is exceptionally thorough and careful.... The author's writing style is very clear and a pleasure to read.
-- William W. Hager, Mathematical 北着Reviews, Issue 98m.
Compare Demmel with the standard work by G. Golub and C. Van Loan, Matrix C四太程级高随促倒阻omputations (艺轮高3rd ed., 1996)... Demmel offers a smaller n花热弦了宽己评为们富umber of topics but focuses on the most impo确章rtant, and p兰rovides o more readable introduction for beginners.
-- B. Borchers, CHOICE, Vol. 35, No. 7, March 1998.
The d差项衡著局益始货星isposition is very much like a series of lect如批苗总ures, new concepts ore introduced precisely where needed...Illustrating examples are 相given, some re建porting really h甲调妒军握色将仍跳eavy computation组同提飞研甚这s, but the autho干湖七服超型r does not shy away from giving mathematical proofs where that is needed...
-- A. Ruh何e, Zeitschrif送活弱功三权往城甚t f?r Mathemat写信种虽米ik und ihre Grenzgebiete, Band 8脸一战设军蒸员会评体79/98.
If you do any computing with matrices-- including linear systems, least squares and eigenvolues-- this book cannot but help you understand what you are doing and why. It presents state-of-the art material (as of June 1997) and can serve as a text or a reference...
-- L. Ehrlich, Computing Reviews, February 1998.
2im Demmel's book on applied numerical linear algebra is a wonderful text blending together the mathematical basis, good numerical software, and practical knowledge for solving real problems. It is destined to be o classic.
-- Jack Dongarra, University of Tennessee, Knoxville.
This is on excellent graduate-level textbook for people who want to learn or teach the state of the art of numerical linear algebra. It covers systematically all the fundamental topics in theory, as well as software implementation. The book is very easy to use in the classroom since it provides pointers, in the book and the author's home page, to lots of available Matlab and LAPACK routines, and it has a large number of homework problems marked Easy, Medium, and Hard. The book requires the students to have a stronger background in linear algebra than most other engineering books on numerical linear algebra.
-- Xia-Chuan Cai, University Of Colorado.
目录
Preface
1 Introduction
1.1 Basic Notation
1.2 Standard Problems of Numerical Linear Algebra
1.3 General Techniques
1.3.1 Matrix Factorizations
1.3.2 Perturbation Theory and Condition Numbers
1.3.3 Effects of Roundoff Error on Algorithms
1.3.4 Analyzing the Speed of Algorithms
1.3.5 Engineering Numerical Software
1.4 Example: Polynomial Evaluation
1.5 Floating Point Arithmetic
1.5.1 Further Details
1.6 Polynomial Evaluation Revisited
1.7 Vector and Matrix Norms
1.8 References and Other Topics for Chapter 1
1.9 Questions for Chapter 1
2 Linear Equation Solving
2.1 Introduction
2.2 Perturbation Theory
2.2.1 Relative Perturbation Theory
2.3 Gaussian Elimination
2.4 Error Analysis
2.4.1 The Need for Pivoting
2.4.2 Formal Error Analysis of Gaussian Elimination
2.4.3 Estimating Condition Numbers
2.4.4 Practical Error Bounds
2.5 Improving the Accuracy of a Solution
2.5.1 Single Precision Iterative Refinement
2.5.2 Equilibration
2.6 Blocking Algorithms for Higher Performance
2.6.1 Basic Linear Algebra Subroutines (BLAS)
2.6.2 How to Optimize Matrix Multiplication
2.6.3 Reorganizing Gaussian Elimination to Use Level 3 BLAS
2.6.4 More About Parallelism and Other Performance Issues.
2.7 Special Linear Systems
2.7.1 Real Symmetric Positive Definite Matrices
2.7.2 Symmetric Indefinite Matrices
2.7.3 Band Matrices
2.7.4 General Sparse Matrices
2.7.5 Dense Matrices Depending on Fewer Than O(n2) Parameters
2.8 References and Other Topics for Chapter 2
2.9 Questions for Chapter 2
3 Linear Least Squares Problems
3.1 Introduction
3.2 Matrix Factorizations That Solve the Linear Least Squares Problem
3.2.1 Normal Equations
3.2.2 QR Decomposition
3.2.3 Singular Value Decomposition
3.3 Perturbation Theory for the Least Squares Problem
3.4 Orthogonal Matrices
3.4.1 Householder Transformations
3.4.2 Givens Rotations
3.4.3 Roundoff Error Analysis for Orthogonal Matrices
3.4.4 Why Orthogonal Matrices?
3.5 Rank-Deficient Least Squares Problems
3.5.1 Solving Rank-Deficient Least Squares Problems Using the SVD
3.5.2 Solving Rank-Deficient Least Squares Problems Using QR with Pivoting
3.6 Performance Comparison of Methods for Solving Least SquaresProblems
3.7 References and Other Topics for Chapter 3
3.8 Questions for Chapter 3
4 Nonsymmetric Eigenvalue Problems
4.1 Introduction
4.2 Canonical Forms
4.2.1 Computing Eigenvectors from the Schur Form
4.3 Perturbation Theory
4.4 Algorithms for the Nonsymmetric Eigenproblem
4.4.1 Power Method
4.4.2 Inverse Iteration
4.4.3 Orthogonal Iteration
4.4.4 QR Iteration
4.4.5 Making QR Iteration Practical
4.4.6 Hessenberg Reduction
……
丛书信息
Springer大学数学图书 (共23册), 这套丛书还有 《数学的读写和证明》,《狭义相对论》,《高性能计算机上的数值线性代数》,《LAPACK95用户指南》,《对称》 等。