Algorithm 776: SRRIT: a Fortran subroutine to calculate the dominant invariant subspace of a nonsymmetric matrix

Authors:
Z. Bai;G. W. Stewart
Affiliations:
Univ. of Kentucky, Lexington;Univ. of Maryland, College Park
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
1997

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Abstract

SRRT is a Fortran program to calculate an approximate orthonomral basis fr a dominant invariant subspace of a real matrix A by the method of simultaneous iteration. Specifically, given an integer m, SRRIT computes a matrix Q with m orthonormal columns and real quasi-triangular matrix T or order m such that the equation AQ = QT is satisfied up to a tolerance specified by the user. The eigenvalues of T are approximations to the m eigenvalues of largest absolute magnitude of A and the columns of Q span the invariant subspace corresponding to those eigenvalues. SRRIT references A only through a user-provided subroutine to form the product AQ; hence it is suitable for large sparse problems.