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39 lines
1.4 KiB
HTML
39 lines
1.4 KiB
HTML
<HTML>
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<!-- DO NOT EDIT: this is a cleared public file -->
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<HEAD>
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<TITLE>Performance of PeIGS</TITLE>
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</HEAD>
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<BODY>
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<H1>Performance of PeIGS</H1>
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<P>
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The numerical method used by PeIGS is bisection for eigenvalues
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and repeated inverse iteration and orthogonalization for eigenvectors.
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Accuracy and orthogonality are similar to
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LAPACK's DSPGV and DSPEV.
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Orthogonality of eigenvectors is enforced even for arbitrarily large
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clusters that span multiple processors.
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<P>
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PeIGS is both fast and scalable -- on a single processor of a KSR-2 it takes
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only 45% longer than LAPACK for a 1000-by-1000 generalized
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eigenproblem, and parallel efficiency is good even for large
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processor counts. For example, in one of our computational chemistry
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applications, the standard eigenproblem Ax = kx was solved for all
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eigenpairs of a 2053-by-2053 matrix. This computation required only 117
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seconds on 150 processors of an Intel Paragon computer, a time-to-solution
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estimated as 77 times faster than the 1 processor time.
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<P>
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PeIGS performance depends to some extent on how eigenvalues cluster
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within the spectrum. Generally speaking, systems with many eigenvalues
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close together take longer to solve due to increased computation and
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communication costs for reorthogonalization. This is an important
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issue because actual applications with large matrices often have
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highly clustered spectra.
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</BODY>
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</HTML>
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