Computer Solution of Linear Algebraic Systems
443 120 1MB
English Pages xii & 148 [162] Year 1967
Table of contents :
Copyright
Preface
Contents
1 Reader's Background And Purpose Of Book
2 Vector And Matrix Norms
3 Diagonal Form Of A Matrix Under Orthogonal Equivalence
4 Proof Of Diagonal-Form Theorem
5 Types Of Computational Problems In Linear Algebra
6 Types Of Matrices Encountered In Practical Problems
7 Sources Of Computational Problems Of Linear Algebra
8 Condition Of A Linear System
9 Gaussian Elimination And Lu Decomposition
10 Need For Interchanging Rows
11 Scaling Equations And Unknowns
12 The Crout And Doolittle Variants
13 Iterative Improvement
14 Computing The Determinant
15 Nearly Singular Matrices
16 Algol 60 Program
17 Fortran, Extended Algol, And Pl/I Programs
18 Matrix Inversion
19 An Example: Hilbert Matrices
20 Floating-Point Round-Off Analysis
21 Rounding Error In Gaussian Elimination
22 Convergence Of Iterative Improvement
23 Positive Definite Matrices; Band Matrices
24 Iterative Methods For Solving Linear Systems
25 Nonlinear Systems Of Equations
Appendix
Bibliography And Author Index
Subject Index
Copyright
Preface
Contents
1 Reader's Background And Purpose Of Book
2 Vector And Matrix Norms
3 Diagonal Form Of A Matrix Under Orthogonal Equivalence
4 Proof Of Diagonal-Form Theorem
5 Types Of Computational Problems In Linear Algebra
6 Types Of Matrices Encountered In Practical Problems
7 Sources Of Computational Problems Of Linear Algebra
8 Condition Of A Linear System
9 Gaussian Elimination And Lu Decomposition
10 Need For Interchanging Rows
11 Scaling Equations And Unknowns
12 The Crout And Doolittle Variants
13 Iterative Improvement
14 Computing The Determinant
15 Nearly Singular Matrices
16 Algol 60 Program
17 Fortran, Extended Algol, And Pl/I Programs
18 Matrix Inversion
19 An Example: Hilbert Matrices
20 Floating-Point Round-Off Analysis
21 Rounding Error In Gaussian Elimination
22 Convergence Of Iterative Improvement
23 Positive Definite Matrices; Band Matrices
24 Iterative Methods For Solving Linear Systems
25 Nonlinear Systems Of Equations
Appendix
Bibliography And Author Index
Subject Index
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