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A Parallelizable Eigensolver for Real Diagonalizable Matrices with Real Eigenvalues
, 1991
"... . In this paper, preliminary research results on a new algorithm for finding all the eigenvalues and eigenvectors of a real diagonalizable matrix with real eigenvalues are presented. The basic mathematical theory behind this approach is reviewed and is followed by a discussion of the numerical consi ..."
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Cited by 31 (6 self)
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. In this paper, preliminary research results on a new algorithm for finding all the eigenvalues and eigenvectors of a real diagonalizable matrix with real eigenvalues are presented. The basic mathematical theory behind this approach is reviewed and is followed by a discussion of the numerical considerations of the actual implementation. The numerical algorithm has been tested on thousands of matrices on both a Cray2 and an IBM RS/6000 Model 580 workstation. The results of these tests are presented. Finally, issues concerning the parallel implementation of the algorithm are discussed. The algorithm's heavy reliance on matrixmatrix multiplication, coupled with the divide and conquer nature of this algorithm, should yield a highly parallelizable algorithm. 1. Introduction. Computation of all the eigenvalues and eigenvectors of a dense matrix is essential for solving problems in many fields. The everincreasing computational power available from modern supercomputers offers the potenti...
Parallel performance of a symmetric eigensolver based on the invariant subspace decomposition approach
 In Proceedings of the 1994 Scalable High Performance Computing Conference
, 1994
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The PRISM Project: Infrastructure and Algorithms for Parallel Eigensolvers
, 1994
"... The goal of the PRISM project is the development of infrastructure and algorithms for the parallel solution of eigenvalue problems. We are currently investigating a complete eigensolver based on the Invariant Subspace Decomposition Algorithm for dense symmetric matrices (SYISDA). After briefly revie ..."
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Cited by 14 (6 self)
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The goal of the PRISM project is the development of infrastructure and algorithms for the parallel solution of eigenvalue problems. We are currently investigating a complete eigensolver based on the Invariant Subspace Decomposition Algorithm for dense symmetric matrices (SYISDA). After briefly reviewing SYISDA, we discuss the algorithmic highlights of a distributedmemory implementation of this approach. These include a fast matrixmatrix multiplication algorithm, a new approach to parallel band reduction and tridiagonalization, and a harness for coordinating the divideandconquer parallelism in the problem. We also present performance results of these kernels as well as the overall SYISDA implementation on the Intel Touchstone Delta prototype. 1. Introduction Computation of eigenvalues and eigenvectors is an essential kernel in many applications, and several promising parallel algorithms have been investigated [29, 24, 3, 27, 21]. The work presented in this paper is part of the PRI...
A Parallel Implementation of the Invariant Subspace Decomposition Algorithm for Dense Symmetric Matrices
, 1993
"... . We give an overview of the Invariant Subspace Decomposition Algorithm for dense symmetric matrices (SYISDA) by first describing the algorithm, followed by a discussion of a parallel implementation of SYISDA on the Intel Delta. Our implementation utilizes an optimized parallel matrix multiplication ..."
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Cited by 13 (2 self)
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. We give an overview of the Invariant Subspace Decomposition Algorithm for dense symmetric matrices (SYISDA) by first describing the algorithm, followed by a discussion of a parallel implementation of SYISDA on the Intel Delta. Our implementation utilizes an optimized parallel matrix multiplication implementation we have developed. Load balancing in the costly early stages of the algorithm is accomplished without redistribution of data between stages through the use of the block scattered decomposition. Computation of the invariant subspaces at each stage is done using a new tridiagonalization scheme due to Bischof and Sun. 1. Introduction Computation of all the eigenvalues and eigenvectors of a dense symmetric matrix is an essential kernel in many applications. The everincreasing computational power available from parallel computers offers the potential for solving much larger problems than could have been contemplated previously. Hardware scalability of parallel machines is freque...