Computer Solution of Linear Algebraic Systems

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