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Numerical Linear Algebra [Hardback]

4.20/5 (10 ratings by Goodreads)
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  • Formāts: Hardback, 271 pages, height x width: 235x155 mm, weight: 1280 g, XI, 271 p., 1 Hardback
  • Sērija : Texts in Applied Mathematics 55
  • Izdošanas datums: 05-Dec-2007
  • Izdevniecība: Springer-Verlag New York Inc.
  • ISBN-10: 0387341595
  • ISBN-13: 9780387341590
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Numerical Linear AlgebraPalielināt
  • Formāts: Hardback, 271 pages, height x width: 235x155 mm, weight: 1280 g, XI, 271 p., 1 Hardback
  • Sērija : Texts in Applied Mathematics 55
  • Izdošanas datums: 05-Dec-2007
  • Izdevniecība: Springer-Verlag New York Inc.
  • ISBN-10: 0387341595
  • ISBN-13: 9780387341590
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780387341590.html
Keywords:
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.A solutions manual is available for instructors.

Unlike the many other textbooks on the topic of linear algebra, this book stands out from the crowd by including mathematical and computational chapters along with examples and exercises with Matlab. In recent years, the use of computers in many areas of engineering and science has made it essential for students to get training in numerical methods and computer programming. Here, the authors use both Matlab and SciLab software as well as covering core standard material. The book is a combination and update of two earlier French books by the authors. One of the key features here 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. This excellent work is intended for libraries; scientists and researchers; pharmaceutical industry.

Recenzijas

From the reviews:





"Allaire (École Polytechnique, France) and Kaber (Université Pierre et Marie Curie, France) taught a numerical linear algebra course to third-year undergraduates; this work, initially published in French, is the culmination of that course. What sets this book apart from others on the subject is its experimental approach in all exercises. For many exercises, the book provides complete solutions including MATLAB scripts . Summing Up: Recommended. Upper-division undergraduates, researchers/faculty, and professionals/practitioners." (J. T. Zerger, CHOICE, Vol. 45 (10), June, 2008)

"The book is concerned with two main aspects from the field of matrix computations: solving linear systems of equations and, respectively, computing eigenvalues and eigenvectors of matrices. It is intended for advanced undergraduate students ." (Constantin Popa, Zentralblatt MATH, Vol. 1135 (13), 2008)

"The textbook Numerical linear algebra is the English translation of the French edition with the same title . The book is divided into eleven chapters. At the end of each chapter some relevant test problems are given. The material presented in the book is very well-organized. This book is an excellent tool for teachers and students." (Zahari Zlatev, Mathematical Reviews, Issue 2008 m)

The present book covers material adequate for students at the end of their undergraduate or the beginning of their graduate years. The presentation is clear and mathematically precise, and solutions to the numerous exercises are provided. Overall, this is a clear and useful introduction into numeral linear algebra. (H. Muthsam, Monatshefte für Mathematik, Vol. 158 (3), November, 2009)

This book was developed for use in a course on numerical linear algebra for third-year undergraduates. The methods are described briefly but clearly. The exercises are one of the main strengths of the book. I can recommend the book as a textbook for undergraduates. (James E. Gentle, SIAM Review, Vol. 52 (1), 2010)

Introduction
1(14)
Discretization of a Differential Equation
1(3)
Least Squares Fitting
4(4)
Vibrations of a Mechanical System
8(2)
The Vibrating String
10(2)
Image Compression by the SVD Factorization
12(3)
Definition and Properties of Matrices
15(30)
Gram-Schmidt Orthonormalization Process
15(2)
Matrices
17(6)
Trace and Determinant
19(1)
Special Matrices
20(1)
Rows and Columns
21(1)
Row and Column Permutation
22(1)
Block Matrices
22(1)
Spectral Theory of Matrices
23(3)
Matrix Triangularization
26(2)
Matrix Diagonalization
28(3)
Min-Max Principle
31(2)
Singular Values of a Matrix
33(5)
Exercises
38(7)
Matrix Norms, Sequences, and Series
45(16)
Matrix Norms and Subordinate Norms
45(7)
Subordinate Norms for Rectangular Matrices
52(2)
Matrix Sequences and Series
54(3)
Exercises
57(4)
Introduction to Algorithmics
61(10)
Algorithms and pseudolanguage
61(3)
Operation Count and Complexity
64(1)
The Strassen Algorithm
65(2)
Equivalence of Operations
67(2)
Exercises
69(2)
Linear Systems
71(26)
Square Linear Systems
71(4)
Over- and Underdetermined Linear Systems
75(1)
Numerical Solution
76(16)
Floating-Point System
77(2)
Matrix Conditioning
79(6)
Conditioning of a Finite Difference Matrix
85(3)
Approximation of the Condition Number
88(3)
Preconditioning
91(1)
Exercises
92(5)
Direct Methods for Linear Systems
97(28)
Gaussian Elimination Method
97(6)
LU Decomposition Method
103(9)
Practical Computation of the LU Factorization
107(1)
Numerical Algorithm
108(1)
Operation Count
108(2)
The Case of Band Matrices
110(2)
Cholesky Method
112(4)
Practical Computation of the Cholesky Factorization
113(1)
Numerical Algorithm
114(1)
Operation Count
115(1)
QR Factorization Method
116(3)
Operation Count
118(1)
Exercises
119(6)
Least Squares Problems
125(18)
Motivation
125(1)
Main Results
126(2)
Numerical Algorithms
128(12)
Conditioning of Least Squares Problems
128(3)
Normal Equation Method
131(1)
QR Factorization Method
132(4)
Householder Algorithm
136(4)
Exercises
140(3)
Simple Iterative Methods
143(20)
General Setting
143(4)
Jacobi, Gauss-Seidel, and Relaxation Methods
147(3)
Jacobi Method
147(1)
Gauss-Seidel Method
148(1)
Successive Overrelaxation Method (SOR)
149(1)
The Special Case of Tridiagonal Matrices
150(4)
Discrete Laplacian
154(2)
Programming Iterative Methods
156(1)
Block Methods
157(2)
Exercises
159(4)
Conjugate Gradient Method
163(28)
The Gradient Method
163(2)
Geometric Interpretation
165(3)
Some Ideas for Further Generalizations
168(3)
Theoretical Definition of the Conjugate Gradient Method
171(3)
Conjugate Gradient Algorithm
174(15)
Numerical Algorithm
178(1)
Number of Operations
179(1)
Convergence Speed
180(2)
Preconditioning
182(4)
Chebyshev Polynomials
186(3)
Exercises
189(2)
Methods for Computing Eigenvalues
191(32)
Generalities
191(1)
Conditioning
192(2)
Power Method
194(4)
Jacobi Method
198(5)
Givens-Householder Method
203(6)
QR Method
209(5)
Lanczos Method
214(5)
Exercises
219(4)
Solutions and Programs
223(42)
Exercises of
Chapter 2
223(11)
Exercises of
Chapter 3
234(3)
Exercises of
Chapter 4
237(4)
Exercises of
Chapter 5
241(9)
Exercises of
Chapter 6
250(7)
Exercises of
Chapter 7
257(1)
Exercises of
Chapter 8
258(2)
Exercises of
Chapter 9
260(2)
Exercises of
Chapter 10
262(3)
References 265(2)
Index 267(5)
Index of Programs 272