| List of Figures |
| List of Tables |
| Preface to Second Edition |
| Preface to First Edition |
| About the Dedication |
| Principles of Finite Precision Computation / 1： |
| Notation and Background / 1.1： |
| Relative Error and Significant Digits / 1.2： |
| Sources of Errors / 1.3： |
| Precision Versus Accuracy / 1.4： |
| Backward and Forward Errors / 1.5： |
| Conditioning / 1.6： |
| Cancellation / 1.7： |
| Solving a Quadratic Equation / 1.8： |
| Computing the Sample Variance / 1.9： |
| Solving Linear Equations / 1.10： |
| Accumulation of Rounding Errors / 1.11： |
| Instability Without Cancellation / 1.12： |
| Increasing the Precision / 1.13： |
| Cancellation of Rounding Errors / 1.14： |
| Rounding Errors Can Be Beneficial / 1.15： |
| Stability of an Algorithm Depends on the Problem / 1.16： |
| Rounding Errors Are Not Random / 1.17： |
| Designing Stable Algorithms / 1.18： |
| Misconceptions / 1.19： |
| Rounding Errors in Numerical Analysis / 1.20： |
| Notes and References / 1.21： |
| Problems |
| Floating Point Arithmetic / 2： |
| Floating Point Number System / 2.1： |
| Model of Arithmetic / 2.2： |
| IEEE Arithmetic / 2.3： |
| Aberrant Arithmetics / 2.4： |
| Exact Subtraction / 2.5： |
| Fused Multiply-Add Operation / 2.6： |
| Choice of Base and Distribution of Numbers / 2.7： |
| Statistical Distribution of Rounding Errors / 2.8： |
| Alternative Number Systems / 2.9： |
| Elementary Functions / 2.10： |
| Accuracy Tests / 2.11： |
| Basics / 2.12： |
| Inner and Outer Products / 3.1： |
| The Purpose of Rounding Error Analysis / 3.2： |
| Running Error Analysis / 3.3： |
| Notation for Error Analysis / 3.4： |
| Matrix Multiplication / 3.5： |
| Complex Arithmetic / 3.6： |
| Miscellany / 3.7： |
| Error Analysis Demystified / 3.8： |
| Other Approaches / 3.9： |
| Summation / 3.10： |
| Summation Methods / 4.1： |
| Error Analysis / 4.2： |
| Compensated Summation / 4.3： |
| Other Summation Methods / 4.4： |
| Statistical Estimates of Accuracy / 4.5： |
| Choice of Method / 4.6： |
| Polynomials / 4.7： |
| Horner's Method / 5.1： |
| Evaluating Derivatives / 5.2： |
| The Newton Form and Polynomial Interpolation / 5.3： |
| Matrix Polynomials / 5.4： |
| Norms / 5.5： |
| Vector Norms / 6.1： |
| Matrix Norms / 6.2： |
| The Matrix p-Norm / 6.3： |
| Singular Value Decomposition / 6.4： |
| Perturbation Theory for Linear Systems / 6.5： |
| Normwise Analysis / 7.1： |
| Componentwise Analysis / 7.2： |
| Scaling to Minimize the Condition Number / 7.3： |
| The Matrix Inverse / 7.4： |
| Extensions / 7.5： |
| Numerical Stability / 7.6： |
| Practical Error Bounds / 7.7： |
| Perturbation Theory by Calculus / 7.8： |
| Triangular Systems / 7.9： |
| Backward Error Analysis / 8.1： |
| Forward Error Analysis / 8.2： |
| Bounds for the Inverse / 8.3： |
| A Parallel Fan-In Algorithm / 8.4： |
| LU Factorization and Linear Equations / 8.5： |
| Gaussian Elimination and Pivoting Strategies / 9.1： |
| LU Factorization / 9.2： |
| The Growth Factor / 9.3： |
| Diagonally Dominant and Banded Matrices / 9.5： |
| Tridiagonal Matrices / 9.6： |
| More Error Bounds / 9.7： |
| Scaling and Choice of Pivoting Strategy / 9.8： |
| Variants of Gaussian Elimination / 9.9： |
| A Posteriori Stability Tests / 9.10： |
| Sensitivity of the LU Factorization / 9.11： |
| Rank-Revealing LU Factorizations / 9.12： |
| Historical Perspective / 9.13： |
| Cholesky Factorization / 9.14： |
| Symmetric Positive Definite Matrices / 10.1： |
| Sensitivity of the Cholesky Factorization / 10.2： |
| Positive Semidefinite Matrices / 10.3： |
| Matrices with Positive Definite Symmetric Part / 10.4： |
| Symmetric Indefinite and Skew-Symmetric Systems / 10.5： |
| Block LDL[superscript T] Factorization for Symmetric Matrices / 11.1： |
| Aasen's Method / 11.2： |
| Block LDL[superscript T] Factorization for Skew-Symmetric Matrices / 11.3： |
| Iterative Refinement / 11.4： |
| Behaviour of the Forward Error / 12.1： |
| Iterative Refinement Implies Stability / 12.2： |
| Block LU Factorization / 12.3： |
| Block Versus Partitioned LU Factorization / 13.1： |
| Error Analysis of Partitioned LU Factorization / 13.2： |
| Error Analysis of Block LU Factorization / 13.3： |
| Matrix Inversion / 13.4： |
| Use and Abuse of the Matrix Inverse / 14.1： |
| Inverting a Triangular Matrix / 14.2： |
| Inverting a Full Matrix by LU Factorization / 14.3： |
| Gauss-Jordan Elimination / 14.4： |
| Parallel Inversion Methods / 14.5： |
| The Determinant / 14.6： |
| Condition Number Estimation / 14.7： |
| How to Estimate Componentwise Condition Numbers / 15.1： |
| The p-Norm Power Method / 15.2： |
| LAPACK 1-Norm Estimator / 15.3： |
| Block 1-Norm Estimator / 15.4： |
| Other Condition Estimators / 15.5： |
| Condition Numbers of Tridiagonal Matrices / 15.6： |
| The Sylvester Equation / 15.7： |
| Solving the Sylvester Equation / 16.1： |
| Backward Error / 16.2： |
| Perturbation Result / 16.3： |
| Stationary Iterative Methods / 16.4： |
| Survey of Error Analysis / 17.1： |
| Singular Systems / 17.2： |
| Stopping an Iterative Method / 17.5： |
| Matrix Powers / 17.6： |
| Matrix Powers in Exact Arithmetic / 18.1： |
| Bounds for Finite Precision Arithmetic / 18.2： |
| Application to Stationary Iteration / 18.3： |
| QR Factorization / 18.4： |
| Householder Transformations / 19.1： |
| Error Analysis of Householder Computations / 19.2： |
| Pivoting and Row-Wise Stability / 19.4： |
| Aggregated Householder Transformations / 19.5： |
| Givens Rotations / 19.6： |
| Gram-Schmidt Orthogonalization / 19.7： |
| Sensitivity of the QR Factorization / 19.9： |
| The Least Squares Problem / 19.10： |
| Perturbation Theory / 20.1： |
| Solution by QR Factorization / 20.2： |
| Solution by the Modified Gram-Schmidt Method / 20.3： |
| The Normal Equations / 20.4： |
| The Seminormal Equations / 20.5： |
| Weighted Least Squares Problems / 20.7： |
| The Equality Constrained Least Squares Problem / 20.9： |
| Proof of Wedin's Theorem / 20.10： |
| Underdetermined Systems / 20.11： |
| Solution Methods / 21.1： |
| Perturbation Theory and Backward Error / 21.2： |
| Vandermonde Systems / 21.3： |
| Primal and Dual Systems / 22.1： |
| Stability / 22.3： |
| Fast Matrix Multiplication / 22.4： |
| Methods / 23.1： |
| The Fast Fourier Transform and Applications / 23.2： |
| The Fast Fourier Transform / 24.1： |
| Circulant Linear Systems / 24.2： |
| Nonlinear Systems and Newton's Method / 24.3： |
| Newton's Method / 25.1： |
| Special Cases and Experiments / 25.2： |
| Automatic Error Analysis / 25.4： |
| Exploiting Direct Search Optimization / 26.1： |
| Direct Search Methods / 26.2： |
| Examples of Direct Search / 26.3： |
| Interval Analysis / 26.4： |
| Other Work / 26.5： |
| Software Issues in Floating Point Arithmetic / 26.6： |
| Exploiting IEEE Arithmetic / 27.1： |
| Subtleties of Floating Point Arithmetic / 27.2： |
| Cray Peculiarities / 27.3： |
| Compilers / 27.4： |
| Determining Properties of Floating Point Arithmetic / 27.5： |
| Testing a Floating Point Arithmetic / 27.6： |
| Portability / 27.7： |
| Avoiding Underflow and Overflow / 27.8： |
| Multiple Precision Arithmetic / 27.9： |
| Extended and Mixed Precision BLAS / 27.10： |
| Patriot Missile Software Problem / 27.11： |
| A Gallery of Test Matrices / 27.12： |
| The Hilbert and Cauchy Matrices / 28.1： |
| Random Matrices / 28.2： |
| "Randsvd" Matrices / 28.3： |
| The Pascal Matrix / 28.4： |
| Tridiagonal Toeplitz Matrices / 28.5： |
| Companion Matrices / 28.6： |
| Solutions to Problems / 28.7： |
| Acquiring Software / B： |
| Internet / B.1： |
| Netlib / B.2： |
| MATLAB / B.3： |
| NAG Library and NAGWare F95 Compiler / B.4： |
| Program Libraries / C： |
| Basic Linear Algebra Subprograms / C.1： |
| EISPACK / C.2： |
| LINPACK / C.3： |
| LAPACK / C.4： |
| The Matrix Computation Toolbox / D： |
| Bibliography |
| List of Figures |
| List of Tables |
| Preface to Second Edition |
図書
