Arbenz Parallel Divide and Conquer Algorithms for the Symmetric Tridiagonal
نویسندگان
چکیده
In this paper a new implementation of a divide and conquer algorithm will be considered. This algorithm, in contrast to the LAPACK algorithm, uses a diierent formulation of the update problem, and extended precision in order to maintain accuracy and orthogonality. Our Intel Paragon implementation shows, in contrast to the Hypercube implementation by Ipsen and Jessup 14], that good speedups can be obtained from a distributed memory parallel version of the divide and conquer eigenvalue algorithm .
منابع مشابه
Parallel block tridiagonalization of real symmetric matrices
Two parallel block tridiagonalization algorithms and implementations for dense real symmetric matrices are presented. Block tridiagonalization is a critical pre-processing step for the block-tridiagonal divide-and-conquer algorithm for computing eigensystems and is useful for many algorithms desiring the efficiencies of block structure in matrices. For an “effectively” sparse matrix, which freq...
متن کاملA Comparison of Parallel Solvers for Diagonally Dominant and General Narrow-Banded Linear Systems
We investigate and compare stable parallel algorithms for solving diagonally dominant and general narrow-banded linear systems of equations. Narrow-banded means that the bandwidth is very small compared with the matrix order and is typically between 1 and 100. The solvers compared are the banded system solvers of ScaLAPACK [11] and those investigated by Arbenz and Hegland [3, 6]. For the diagon...
متن کاملNew fast divide-and-conquer algorithms for the symmetric tridiagonal eigenvalue problem
In this paper, two accelerated divide-and-conquer algorithms are proposed for the symmetric tridiagonal eigenvalue problem, which cost O(Nr) flops in the worst case, where N is the dimension of the matrix and r is a modest number depending on the distribution of eigenvalues. Both of these algorithms use hierarchically semiseparable (HSS) matrices to approximate some intermediate eigenvector mat...
متن کاملUnified Framework for the Parallelization of Divide and Conquer Based Tridiagonal Systems
In this paper we describe a method for the regularization and parallelization of tridiagonal algorithms based on the divide and conquer strategy. The method is based on perfect shuffle and unshuffle permutations which transform the flow of these algorithms into a flow with the same pattern of communications in all the stages (constant geometry). We use a unified parallel architecture defined by...
متن کاملAn O(N2 ) Method for Computing the Eigensystem of N ˟ N Symmetric Tridiagonal Matrices by the Divide and Conquer Approach
An efficient method to solve the eigenproblem of N x N symmetric tridiagonal matrices is proposed. Unlike the standard eigensolvers that necessitate O(N3) operations to compute the eigenvectors of such matrices, the proposed method computes both the eigenvalues and eigenvectors with only O(N2) operations. The method is based on serial implementation of the recently introduced Divide and Conquer...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1994