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Parallel performance of a symmetric eigensolver based on the invariant subspace decomposition approach
 In Scalable High Performance Computing Conference
, 1994
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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 14 (4 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.
Fast Spectral Projection Algorithms
, 1998
"... 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 Kohn–Sham iteration, and so obtain the electron density. We compute the spectral projector by constructing the matrix sign function through a simpl ..."
Abstract
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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 Kohn–Sham 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 space–spatialfrequency 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. c ° 1999 Academic Press Key Words: spectral projectors; density matrix; fast algorithms; wavelets; partitioned SVD.
On the Design of a Tridiagonalization Routine for Banded Matrices
"... This paper discusses scalability and data layout issues arising in the development of a parallel algorithm for reducing a banded matrix to tridiagonal form. As it turns out, balancing the memory and computational complexity of the reduction of the matrix and the accumulation of the associated orthog ..."
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This paper discusses scalability and data layout issues arising in the development of a parallel algorithm for reducing a banded matrix to tridiagonal form. As it turns out, balancing the memory and computational complexity of the reduction of the matrix and the accumulation of the associated orthogonal matrix is the key to scalability and sustained performance. 1 Introduction Reduction to tridiagonal form is a major step in eigenvalue computations for symmetric matrices. If the matrix is full, the conventional Householder tridiagonalization approach [7, p. 276] or block variants thereof [6] is the usual method of choice. Another approach is the successive bandreduction (SBR) approach [4], which in its simplest form first reduces a matrix to narrow banded form and from there to tridiagonal form. As is shown in [2], such an approach can also advantageously used for a "rankrevealing tridiagonalization" as it is, for example, required, in the invariant subspace decomposition approach (I...