Jan Ole Aasen. On the reduction of a symmetric matrix to tridiagonal form. BIT, 11:233--242, 1971. Home/Search Document Not in Database Summary Related Articles Check |
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Stability of Block LDL^T Factorization of a Symmetric Tridiagonal .. - Higham (1998) (Correct)
....growth factor, numerical stability, rounding error analysis, LAPACK, LINPACK. AMS subject classifications. primary 65F05, 65G05 1 Introduction Linear systems involving symmetric indefinite tridiagonal matrices arise in a number of situations. For example, Aasen s method with partial pivoting [1] produces a factorization PiA Pi = LTL of a symmetric matrix A, where Pi is a permutation matrix, L is unit lower triangular, and T is tridiagonal. To solve a linear system Ax = b using Aasen s method it is necessary to solve a system with coefficient matrix T . A recent application that ....
Jan Ole Aasen. On the reduction of a symmetric matrix to tridiagonal form. BIT, 11:233--242, 1971.
Notes on Accuracy and Stability of Algorithms in Numerical Linear .. - Higham (1998) (Correct)
....does not identify clear superiority of the BBK strategy. Therefore with the available evidence it is not possible to conclude that the BBK strategy has superior accuracy or stability to the BK strategy for solving general symmetric indefinite linear systems. 3.2. Aasen s Method Aasen s method [1] factorizes a symmetric matrix A 2 R where L is unit lower triangular with first column e 1 , T = 6 6 6 6 6 ff 1 fi 1 fi 1 ff 2 fi 2 . fi n Gamma1 fi n Gamma1 ff n 7 7 7 7 7 is tridiagonal, and P is a permutation matrix. To derive Aasen s ....
....we compute v k = ff ki Gamma l kj h ji , k = i 1: n, find r such that jv r j = maxf jv k j : k = i 1: n g, and then swap v k and v r and make corresponding interchanges in A and L. This partial pivoting strategy ensures that jl ij j 1 for i j. 3.2.1. Rounding Error Analysis Aasen [1] states without proof a backward error bound for the factorization. We give a detailed analysis of the factorization and the subsequent solution of a linear system. We will ignore pivoting (or, equivalently, assume that A is pre pivoted ) The Factorization We wish to bound the residual A ....
Jan Ole Aasen. On the reduction of a symmetric matrix to tridiagonal form. BIT, 11:233--242, 1971.
Stability of Block LDL^T Factorization of a Symmetric Tridiagonal .. - Higham (1998) (Correct)
....growth factor, numerical stability, rounding error analysis, LAPACK, LINPACK. AMS subject classifications. primary 65F05, 65G05 1 Introduction Linear systems involving symmetric indefinite tridiagonal matrices arise in a number of situations. For example, Aasen s method with partial pivoting [1] produces a factorization PiA Pi T = LTL T of a symmetric matrix A, where Pi is a permutation matrix, L is unit lower triangular, and T is tridiagonal. To solve a linear system Ax = b using Aasen s method it is necessary to solve a system with coefficient matrix T . A recent application ....
Jan Ole Aasen. On the reduction of a symmetric matrix to tridiagonal form. BIT, 11:233--242, 1971.
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