Numerical Computation 2

• 10 Best Approximation.- 10.1 Mathematical Foundations.- 10.2 Continuous Least Squares Approximation.- 10.3 Discrete Least Squares Approximation.- 10.4 Uniform Best Approximation.- 10.5 Approximation Algorithms.- 10.6 Approximation Software for Special Functions.- 11 The Fourier Transform.- 11.1 Background.- 11.2 Mathematical Foundations.- 11.3 Trigonometric Interpolation.- 11.4 Convolution.- 11.5 Manipulation of the Signal Spectrum.- 11.6 DFT Algorithms.- 11.7 FFT Software Packages.- 11.8 FFT Routines in Software Libraries.- 11.9 Other FFT Programs.- 12 Numerical Integration.- 12.1 Fundamentals of Integration.- 12.2 Preprocessing of Integration Problems.- 12.3 Univariate Integration Formulas.- 12.4 Multivariate Integration Formulas.- 12.5 Integration Algorithms.- 13 Systems of Linear Equations.- 13.1 Design Stage.- 13.2 Realization Stage.- 13.3 Verification Stage.- 13.4 Mathematical Foundations.- 13.5 Special Properties of Matrices.- 13.6 Special Types of Matrices.- 13.7 Singular Value Decomposition.- 13.8 The Condition of Linear Systems.- 13.9 Condition of Least Squares Problems.- 13.10 Condition Analysis Using the SVD.- 13.11 Direct Methods.- 13.12 Special Types of Linear Systems.- 13.13 Assessment of the Accuracy Achieved.- 13.14 Methods for Least Squares Problems.- 13.15 LAPACK—The Fundamental Linear Algebra Package.- 13.16 LAPACK Black Box Programs.- 13.17 LAPACK Computational Routines.- 13.18 LAPACK Documentation.- 13.19 LAPACK Storage Schemes.- 13.20 Block Size for Block Algorithms.- 13.21 LAPACK Variants and Extensions.- 14 Nonlinear Equations.- 14.1 Iterative Methods.- 14.2 Nonlinear Scalar Equations.- 14.3 Systems of Nonlinear Equations.- 14.4 Nonlinear Data Fitting.- 15 Eigenvalues and Eigenvectors.- 15.1 Mathematical Foundations.- 15.2 Condition ofEigenvalue Problems.- 15.3 The Power Method.- 15.4 The QR Algorithm.- 15.5 The Diagonal Reduction.- 15.6 The Hessenberg Reduction.- 15.7 LAPACK Programs.- 16 Large, Sparse Linear Systems.- 16.1 Storage Schemes for Iterative Methods.- 16.2 Storage Schemes for Symmetric Matrices.- 16.3 Storage Schemes for Direct Methods.- 16.4 Comparison of Storage Schemes.- 16.5 Direct Methods.- 16.6 Iterative Methods.- 16.7 Minimization Methods.- 16.8 Stationary Iterative Methods.- 16.9 Non-Stationary Iterative Methods.- 16.10 Preconditioning.- 16.11 Matrix-Vector Products.- 16.12 Parallelism.- 16.13 Selecting an Iterative Method.- 16.14 Software for Sparse Systems.- 16.15 Basic Software.- 16.16 Dedicated Software Packages.- 16.17 Routines from Software Libraries.- 17 Random Numbers.- 17.1 Random Number Generators.- 17.2 The Generation of Uniform Random Numbers.- 17.3 The Generation of Non-uniform Random Numbers.- 17.4 Testing Random Number Generators.- 17.5 Software for Generating Random Numbers.- Glossary of Notation.- Author Index.

"The two volumes can be highly recommended for newcomers in the area as well as for people working for a long time in or with computer numerics."  EUROSIM - Simulation News Europe "... This book is highly recommended to students, scientists, anad engineers interested in the numerical solution of mathematical problems. It is very useful as a handbook for both newcomers and experts. Every science/engineering/mathematics/computer science library should have a copy of this book."Matti Vuorinen, Mathematical Reviews 2003