Author | Wilkinson, J. H. author |
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Title | Handbook for Automatic Computation [electronic resource] : Volume II: Linear Algebra / by J. H. Wilkinson, C. Reinsch ; edited by F. L. Bauer, A. S. Householder, F. W. J. Olver, H. Rutishauser, K. Samelson, E. Stiefel |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1971 |
Connect to | http://dx.doi.org/10.1007/978-3-642-86940-2 |
Descript | IX, 441 p. online resource |
I Linear Systems, Least Squares and Linear Programming -- to Part I (J. H. Wilkinson) . -- 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) -- Contribution II/l: The Jacobi Method for Real Symmetric Matrices -- Contribution II/2: Householderโs 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