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We present a parallel implementation of the block-tridiagonal divide-and-conquer algorithm that computes eigensolutions of symmetric block-tridiagonal matrices to reduced accuracy. In our implementation, we use mixed data/task parallelism to achieve data distribution and workload balance. Numerical tests show that our implementation is efficient, scalable(More)
A divide-and-conquer method for computing eigenvalues and eigenvectors of a block-tridiagonal matrix with rank-one off-diagonal blocks is presented. The implications of unbalanced merging operations due to unequal block sizes are analyzed and illustrated with numerical examples. It is shown that an unfavorable order for merging blocks in the synthesis phase(More)
A block tridiagonalization algorithm is proposed for transforming a sparse (or "effectively" sparse) symmetric matrix into a related block tridiagonal matrix, such that the eigenvalue error remains bounded by some prescribed accuracy tolerance. It is based on a heuristic for imposing a block tridiagonal structure on matrices with a large percentage of zero(More)
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 "(More)
I am submitting herewith a dissertation written by Yihua Bai entitled " High Performance Parallel Approximate Eigensolver for Real Symmetric Matrices. " I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the requirements for the degree of Doctor of Philosophy, with(More)
This paper presents an overview of the major computational problems in numerical linear algebra and indicates their connection to the "mission-oriented" projects of the Department of Energy. A nontechnical introduction section outlines the topic and presents the major considerations in developing tools for solving these problems. The remaining sections(More)