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Parallel Performance of a Symmetric Eigensolver based on the Invariant Subspace Decomposition Approach
, 1994
"... In this paper, we discuss work in progress on a complete eigensolver based on the Invariant Subspace Decomposition Algorithm for dense symmetric matrices (SYISDA). We describe a recently developed acceleration technique that substantially reduces the overall work required by this algorithm and revie ..."
Abstract

Cited by 15 (0 self)
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In this paper, we discuss work in progress on a complete eigensolver based on the Invariant Subspace Decomposition Algorithm for dense symmetric matrices (SYISDA). We describe a recently developed acceleration technique that substantially reduces the overall work required by this algorithm and review 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 present performance results for the dominant kernel, dense matrix multiplication, as well as for the overall SYISDA implementation on the Intel Touchstone Delta and the Intel Paragon. 1. Introduction Computation of eigenvalues and eigenvectors is an essential kernel in many applications, and several promising parallel algorithms have been investigated [26, 3, 28, 22, 25, 6]. The work presented in t...
Fast spectral projection algorithms for densitymatrix computations
 J. Comput. Phys
, 1999
"... We present a fast algorithm for the construction of a spectral projector. This algorithm allows us to compute the density matrix, as used in e.g the KohnSham iteration, and so obtain the electron density. We compute the spectral projector by constructing the matrix sign function through a simple po ..."
Abstract

Cited by 7 (3 self)
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We present a fast algorithm for the construction of a spectral projector. This algorithm allows us to compute the density matrix, as used in e.g the KohnSham iteration, and so obtain the electron density. We compute the spectral projector by constructing the matrix sign function through a simple polynomial recursion. We present several matrix representations for fast computation within this recursion, using bases with controlled spacespatial frequency localization. In particular we consider wavelet and local cosine bases. Since spectral projectors appear in many contexts, we expect many additional applications of our approach. Subject Classification: 65D15 65T99 81C06 42C99 Keywords: spectral projectors, density matrix, fast algorithms, wavelets, partitioned SVD.