Numerical Linear Algebra

Front Cover
Springer Science & Business Media, Dec 17, 2008 - Mathematics - 271 pages
1 Review

This book distinguishes itself from the many other textbooks on the topic of linear algebra 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. It is intended for libraries; scientists and researchers; pharmaceutical industry.

 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Introduction
1
12 Least Squares Fitting
4
13 Vibrations of a Mechanical System
8
14 The Vibrating String
10
15 Image Compression by the SVD Factorization
12
Definition and Properties of Matrices
15
22 Matrices
17
221 Trace and Determinant
19
72 Main Results
126
73 Numerical Algorithms
128
732 Normal Equation Method
131
733 QR Factorization Method
132
734 Householder Algorithm
136
74 Exercises
140
Simple Iterative Methods
143
82 Jacobi GaussSeidel and Relaxation Methods
147

222 Special Matrices
20
223 Rows and Columns
21
224 Row and Column Permutation
22
23 Spectral Theory of Matrices
23
24 Matrix Triangularization
26
25 Matrix Diagonalization
28
26 MinMax Principle
31
27 Singular Values of a Matrix
33
28 Exercises
38
Matrix Norms Sequences and Series
45
32 Subordinate Norms for Rectangular Matrices
52
33 Matrix Sequences and Series
54
34 Exercises
57
Introduction to Algorithmics
61
42 Operation Count and Complexity
64
43 The Strassen Algorithm
65
44 Equivalence of Operations
67
45 Exercises
69
Linear Systems
71
52 Over and Underdetermined Linear Systems
75
53 Numerical Solution
76
531 FloatingPoint System
77
532 Matrix Conditioning
79
533 Conditioning of a Finite Difference Matrix
85
534 Approximation of the Condition Number
88
535 Preconditioning
91
54 Exercises
92
Direct Methods for Linear Systems
97
62 LU Decomposition Method
103
621 Practical Computation of the LU Factorization
107
622 Numerical Algorithm
108
624 The Case of Band Matrices
110
63 Cholesky Method
112
631 Practical Computation of the Cholesky Factorization
113
632 Numerical Algorithm
114
633 Operation Count
115
64 QR Factorization Method
116
641 Operation Count
118
65 Exercises
119
Least Squares Problems
125
822 GaussSeidel Method
148
823 Successive Overrelaxation Method SOR
149
83 The Special Case of Tridiagonal Matrices
150
84 Discrete Laplacian
154
85 Programming Iterative Methods
156
86 Block Methods
157
87 Exercises
159
Conjugate Gradient Method
163
92 Geometric Interpretation
165
93 Some Ideas for Further Generalizations
168
94 Theoretical Definition of the Conjugate Gradient Method
171
95 Conjugate Gradient Algorithm
174
951 Numerical Algorithm
178
952 Number of Operations
179
953 Convergence Speed
180
954 Preconditioning
182
955 Chebyshev Polynomials
186
96 Exercises
189
Methods for Computing Eigenvalues
191
102 Conditioning
192
103 Power Method
194
104 Jacobi Method
198
105 GivensHouseholder Method
203
106 QR Method
209
107 Lanczos Method
214
108 Exercises
219
Solutions and Programs
223
112 Exercises of Chapter 3
234
113 Exercises of Chapter 4
237
114 Exercises of Chapter 5
241
115 Exercises of Chapter 6
250
116 Exercises of Chapter 7
257
117 Exercises of Chapter 8
258
118 Exercises of Chapter 9
260
119 Exercises of Chapter 10
262
References
265
Index
266
Index of Programs
272
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information