EIGENTEST: A Test Matrix Generator for Large-Scale Eigenproblems
EIGENTEST: A Test Matrix Generator for Large-Scale Eigenproblems
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Date
2006-02-13T19:44:17Z
Authors
Lee, Che Rung
Stewart, G. W.
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Abstract
Eigentest is a package that produces real test matrices with known
eigensystems. A test matrix, called an eigenmat, is generated in a
factored form, in which the user can specify the eigenvalues and has
some control over the condition of the eigenvalues and eigenvectors.
An eigenmat A of order n requires only O(n) storage for its
representation. Auxiliary programs permit the computation of
(A - sI)*b, (A - sI)'*b, inv(A - sI)*b, and inv(A - sI)*b in O(n)
operations. A special routine computes specified eigenvectors of an
eigenmat and the condition of its eigenvalue. Thus eigenmats are
suitable for testing algorithms based on Krylov sequences, as well as
others based on matrix-vector products. This paper introduces the
eigenmat and describes implementations in Fortran~77, Fortran~95, C,
and Matlab.