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...
متن کاملA Parallel Algorithm for the Reduction of a Nonsymmetric Matrix to Block Upper-Hessenberg Form
In this paper, we present an algorithm for the reduction to block upper-Hessenberg form which can be used to solve the nonsymmetric eigenvalue problem on message-passing multicomputers. On such multicomputers, a nonsymmetric matrix can be distributed across processing nodes logically configured into a two-dimensional mesh using the block-cyclic data distribution. Based on the matrix partitionin...
متن کاملReduction of a Regular Matrix Pair (A, B) to Block Hessenberg Triangular Form
An algorithm for reduction of a regular matrix pair (A; B) to block Hessenberg-triangular form is presented. This condensed form Q T (A; B)Z = (H; T), where H and T are block upper Hessenberg and upper triangular, respectively, and Q and Z orthogonal, may serve as a rst step in the solution of the generalized eigenvalue problem Ax = Bx. It is shown how an elementwise algorithm can be reorganize...
متن کاملEfficient Reduction from Block Hessenberg Form to Hessenberg Form Using Shared Memory
A new cache-efficient algorithm for reduction from block Hessenberg form to Hessenberg form is presented and evaluated. The algorithm targets parallel computers with shared memory. One level of look-ahead in combination with a dynamic load-balancing scheme significantly reduces the idle time and allows the use of coarse-grained tasks. The coarse tasks lead to high-performance computations on ea...
متن کاملBlocked Algorithms for the Reduction to Hessenberg-triangular Form Revisited
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...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1969
ISSN: 0025-5718
DOI: 10.2307/2004967