Handbook for Automatic Computation

I Linear Systems, Least Squares and Linear Programming.- to Part I (J. H. Wilkinson) ..- 1. Introduction.- 2. List of Procedures.- 3. Positive Definite Symmetric Matrices.- 4. Non-Positive Definite Symmetric Matrices.- 5. Non-Hermitian Matrices.- 6. Least Squares and Related Problems.- 7. The Linear Programming Problem.- Contribution I/1: Symmetric Decomposition of a Positive Definite Matrix.- Contribution I/2: Iterative Refinement of the Solution of a Positive Definite System of Equations.- Contribution I/3: Inversion of Positive Definite Matrices by the Gauss-Jordan Method.- Contribution I/4: Symmetric Decomposition of Positive Definite Band Matrices.- Contribution I/5: The Conjugate Gradient Method.- Contribution 1/6: Solution of Symmetric and Unsymmetric Band Equations and the Calculation of Eigenvectors of Band Matrices.- Contribution I/7: Solution of Real and Complex Systems of Linear Equations.- Contribution I/8: Linear Least Squares Solutions by Householder Transformations.- Contribution I/9: Elimination with Weighted Row Combinations for Solving Linear Equations and Least Squares Problems.- Contribution I/l0: Singular Value Decomposition and Least Squares Solutions.- Contribution I/l l: A Realization of the Simplex Method based on Triangular Decompositions.- II The Algebraic Eigenvalue Problem.- to Part II (J. H. Wilkinson).- 1. Introduction.- 2. List of Procedures.- 3. Real, Dense, Symmetric Matrices.- 4. Symmetric Band Matrices.- 5. Simultaneous Determination of Dominant Eigenvalues and Eigenvectors of a Symmetric Sparse Matrx.- 6. The Generalized Symetric Eigenvalue Problems Ax=?Bx and ABx = ?.- 7. Hermitian Matrices.- 8. Real Dense Unsymmetric Matrices.- 9. Unsymmetric Band Matrices.- 10. Dense Unsymmetric Matrices with Complex Elements.- Contribution II/l: The Jacobi Method for Real Symmetric Matrices.- Contribution II/2: Householder’s Tridiagonalization of a Symmetric Matrix.- Contribution II/3: The QR and QL Algorithms for Symmetric Matrices.- Contribution II/4: The Implicit QL Algorithm.- Contribution II/5: Calculation of the Eigenvalues of a Symmetric Tridiagonal Matrix by the Method of Bisection.- Contribution II/6: Rational Q R Transformation with Newton Shift for Symmetric TridiagonalMatrices.- Contribution II/7: The QR Algorithm for Band Symmetric Matrices.- Contribution II/8: Tridiagonalization of a Symmetric Band Matrix.- Contribution II/9: Simultaneous Iteration Method for Symmetric Matrices.- Contribution II/l0: Reduction of the Symmetric Eigenproblem A x =?Bx and Related Problems to Standard Form.- Contribution II/11: Balancing a Matrix for Calculation of Eigenvalues and Eigenvectors.- Contribution II/12: Solution to the Eigenproblem by a Norm Reducing Jacobi Type Method.- Contribution II/13: Similarity Reduction of a General Matrix to Hessenberg Form.- Contribution II/14: The QR Algorithm for Real Hessenberg Matrices.- Contribution II/15: Eigenvectors of Real and Complex Matrices by L R and Q R triangulari.- Contribution II/16: The Modified L R Algorithm for Complex Hessenberg Matrices.- Contribution II/l 7: Solution to the Complex Eigenproblem by a Norm Reducing Jacobi Type Method.- Contribution II/l 8: The Calculation of Specified Eigenvectors by Inverse Iteration.