Perturbation analysis of system hessenberg and hessenberg-triangular forms
نویسندگان
چکیده
منابع مشابه
Parallel Reduction of a Block Hessenberg-Triangular Matrix Pair to Hessenberg-Triangular Form—Algorithm Design and Performance Results
The design, implementation and performance of a parallel algorithm for reduction of a matrix pair in block upper Hessenberg-Triangular form (Hr, T ) to upper Hessenberg-triangular form (H, T ) is presented. This reduction is the second stage in a two-stage reduction of a regular matrix pair (A, B) to upper Hessenberg-Triangular from. The desired upper Hessenberg-triangular form is computed usin...
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The QZ algorithm for computing eigenvalues and eigenvectors of a matrix pencil A − λB requires that the matrices first be reduced to Hessenberg-triangular (HT) form. The current method of choice for HT reduction relies entirely on Givens rotations partially accumulated into small dense matrices which are subsequently applied using matrix multiplication routines. A non-vanishing fraction of the ...
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We present two variants of Moler and Stewart’s algorithm for reducing a matrix pair to Hessenberg-triangular (HT) form with increased data locality in the access to the matrices. In one of these variants, a careful reorganization and accumulation of Givens rotations enables the use of efficient level 3 BLAS. Experimental results on four different architectures, representative of current high pe...
متن کاملParallel Reduction from Block Hessenberg to Hessenberg using MPI
In many scientific applications, eigenvalues of a matrix have to be computed. By first reducing a matrix from fully dense to Hessenberg form, eigenvalue computations with the QR algorithm become more efficient. Previous work on shared memory architectures has shown that the Hessenberg reduction is in some cases most efficient when performed in two stages: First reduce the matrix to block Hessen...
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We present methods for improving data reuse in solving sequences of linear systems that are Hessenberg matrices shifted by a sequence of scalars times the identity or a triangular matrix. The methods take into consideration the robust handling of overrow and include new condition estimation strategies. We provide timings on both scalar and vector machines to demonstrate both the diversity and i...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1996
ISSN: 0024-3795
DOI: 10.1016/0024-3795(95)00107-7