Linear algebra

Front Matter....Pages I-IX
Front Matter....Pages 1-8
Symmetric Decomposition of a Positive Definite Matrix....Pages 9-30
Iterative Refinement of the Solution of a Positive Definite System of Equations....Pages 31-44
Inversion of Positive Definite Matrices by the Gauss-Jordan Method....Pages 45-49
Symmetric Decomposition of Positive Definite Band Matrices....Pages 50-56
The Conjugate Gradient Method....Pages 57-69
Solution of Symmetric and Unsymmetric Band Equations and the Calculations of Eigenvectors of Band Matrices....Pages 70-92
Solution of Real and Complex Systems of Linear Equations....Pages 93-110
Linear Least Squares Solutions by Housholder Transformations....Pages 111-118
Elimination with Weighted Row Combinations for Solving Linear Equations and Least Squares Problems....Pages 119-133
Singular Value Decomposition and Least Squares Solutions....Pages 134-151
A Realization of the Simplex Method Based on Triangular Decompositions....Pages 152-190
Front Matter....Pages 191-201
The Jacobi Method for Real Symmetric Matrices....Pages 202-211
Householder’s Tridiagonalization of a Symmetric Matrix....Pages 212-226
The QR and QL Algorithms for Symmetric Matrices....Pages 227-240
The Implicit QL Algorithm....Pages 241-248
Calculation of the Eigenvalues of a Symmetric Tridiagonal Matrix by the Method of Bisection....Pages 249-256
Rational QR Transformation with Newton Shift for Symmetric Tridiagonal Matrices....Pages 257-265
The QR Algorithm for Band Symmetric Matrices....Pages 266-272
Tridiagonalization of a Symmetric Band Matrix....Pages 273-283
Simultaneous Iteration Method for Symmetric Matrices....Pages 284-302
Front Matter....Pages 191-201
Reduction of the Symmetric Eigenproblem Ax = λBx and Related Problems to Standard Form....Pages 303-314
Balancing a Matrix for Calculation of Eigenvalues and Eigenvectors....Pages 315-326
Solution to the Eigenproblem by a Norm Reducing Jacobi Type Method....Pages 327-338
Similarity Reduction of a General Matrix to Hessenberg Form....Pages 339-358
The QR Algorithm for Real Hessenberg Matrices....Pages 359-371
Eigenvectors of Real and Complex Matrices by LR and QR triangularizations....Pages 372-395
The Modified LR Algorithm for Complex Hessenberg Matrices....Pages 396-403
Solution to the Complex Eigenproblem by a Norm Reducing Jacobi Type Method....Pages 404-417
The Calculation of Specified Eigenvectors by Inverse Iteration....Pages 418-439
Back Matter....Pages 440-441