Short description The perfect combination: a complete and scientifically accurate description of numerical algorithms that actually work, and a how-to guide to using them for practical problems in engineering and applied mathematics.
From the contents Preface BASIC CONCEPTS Introduction Modeling Physical Phenomena Number Representation on the Computer Elementary Operations Error Sources Error Propagation Decision-Making for an Optimal Program Selection of Programming Languages: Why C++?
SOME UTILITIES IN THE BzzMATH LIBRARY Introduction Messages and Printing Save and Load Integer Algebra BzzVevtorIntArray and BzzVectorArray BzzMatrixCoefficientsExistence BzzMatrixExistence BzzSymmetricMatrixCoefficientsExistence Complex Numbers Miscellaneous Utilities BzzPlot.exe and BzzPlotSparse.exe
LINEAR ALGEBRA Introduction Classes for Linear Algebra BzzVector Class BzzMatrix Class Vector and Matrix Norms Structured Matrices Sparse Unstructured Matrices Symmetric Matrices Linear Algebra Operations
SQUARE LINEAR SYSTEMS Introduction Gauss Elimination Gauss Transformation Classical Gauss Factorization Alternative Methods Conditioning of Linear Systems Best Pivot Selection Solution Features Class for Linear System Solution Condition Number Computation Determinant Evaluation Inverse Matrix Sparse Matrices Classes for Linear System Solution with Sparse Unstructured Matrices
STRUCTURED LINEAR SYSTEMS Introduction Symmetric Matrices Symmetric Sparse Matrices Band Matrices Diagonal Block Matrices Iterative Methods Systems Generated by Special Physical Problems
OVERDIMENSIONED LINEAR SYSTEMS Introduction Orthogonal Matrices Problem Conditioning Method of Least Squares Orthogonal Transformation QR Factorization Classes for QRT Factorization SVC Factorization Class for SVD Factorization Advantages of SVD Factorization
UNDERDIMENSIONED LINEAR SYSTEMS Introduction LQ Factorization Classes for LQ Factorization Null Space Minimization with Linear Constraints Minimizing a Sum of Squares Subject to Linear Constraints Special Problems Solved by LQ Factorization
EIGENVALUES AND EIGENVECTORS FOR SYMMETRIC MATRICES Introduction Eigenvalues of Symmetric Matrices Power Method Inverse Power Method Inverse-Translate Power Method Jacobi Method QR Algorithm Eigenvalues of Rank-2 Matrices
ITERATIVE PROCESSES Introduction Convergence of an Iterative Algorithm Convergence Speed Convergence Accelerators Extrapolation Extrapolation Methods Class for Numerical Derivation
APPENDIX A: Matrix Product APPENDIX B: Entertainment APPENDIX C: Basic Requirements for Using the BzzMath Library APPENDIX D: Copyrights
