Handbook for Automatic Computation: Volume 2: Linear Algebra (Grundlehren der mathematischen Wissenschaften)

Title Page......Page img001_2R.djvu
Copyright......Page img002_1L.djvu
Preface......Page img002_2R.djvu
Contents......Page img003_2R.djvu
Introduction......Page img005_2R.djvu
Contribution I/1 Symmetric Decomposition of a Positive Definite Matrix ......Page img009_2R.djvu
Contribution I/2 Iterative Refinement of the Solution  of a Positive Definite System of Equations......Page img020_2R.djvu
Contribution I/3 Inversion of Positive Definite Matrices by the Gauss-Jordan Method  ......Page img027_2R.djvu
Contribution I/4 Symmetric Decomposition of Positive Definite Band Matrices......Page img030_1L.djvu
Contribution I/5 The Conjugate Gradient Method ......Page img033_2R.djvu
Contribution I/6 Solution of Symmetric and Unsymmetric Band Equations and the Calculations of Eigenvectors of Band Matrices......Page img040_1L.djvu
Contribution I/7 Solution of Real and Complex Systems of Linear Equations......Page img051_2R.djvu
Contribution I/8 Linear Least Squares Solutions by Housholder Transformations......Page img060_2R.djvu
Contribution I/9 Elimination with Weighted Row Combinations for Solving Linear Equations and Least Squares Problems......Page img064_2R.djvu
Contribution I/10 Singular Value Decomposition and Least Squares Solutions......Page img072_1L.djvu
Contribution I/11 A Realization of the Simplex Method Based on Triangular Decompositions  ......Page img081_1L.djvu
Introduction......Page img100_2R.djvu
Contribution II/1 The Jacobi Method for Real Symmetric Matrices......Page img106_1L.djvu
Contribution II/2 Householder\'s Tridiagonalization of a Symmetric Matrix......Page img111_1L.djvu
Contribution II/3 The QR and QL Algorithms for Symmetric Matrices......Page img118_2R.djvu
Contribution II/4 The Implicit QL Algorithm......Page img125_2R.djvu
Contribution II/5 Calculation of the Eigenvalues of a Symmetric Tridiagonal Matrix by the Method of Bisection......Page img129_2R.djvu
Contribution II/6  Rational QR Transformation with Newton Shift for Symmetric Tridiagonal Matrices* ......Page img133_2R.djvu
Contribution II/7 The QR Algorithm for Band Symmetric Matrices......Page img138_1L.djvu
Contribution II/8 Tridiagonalization of a Symmetric Band Matrix......Page img141_2R.djvu
Contribution II/9 Simultaneous Iteration Method for Symmetric Matrices......Page img147_1L.djvu
Contribution II/10  Reduction of the Symmetric Eigenproblem Ax =(lambda)Bx and Related Problems to Standard Form......Page img156_2R.djvu
Contribution II/11 Balancing a Matrix for Calculation of Eigenvalues and Eigenvectors......Page img162_2R.djvu
Contribution II/12 Solution to the Eigenproblem by a Norm Reducing Jacobi Type Method......Page img168_2R.djvu
Contribution II/13 Similarity Reduction of a General Matrix to Hessenberg Form......Page img174_2R.djvu
Contribution II/14 The QR Algorithm for Real Hessenberg Matrices......Page img184_2R.djvu
Contribution II/15 Eigenvectors of Real and Complex Matrices by LR and QR triangularizations......Page img191_1L.djvu
Contribution II/16The Modified LR Algorithm for Complex Hessenberg Matrices ......Page img203_1L.djvu
Contribution II/17 Solution to the Complex Eigenproblem by a Norm Reducing Jacobi Type Method......Page img207_1L.djvu
Contribution II/18 The Calculation of Specified Eigenvectors by Inverse Iteration  ......Page img214_1L.djvu