Accession Number : ADA018432

Title :   An O(n squared) Algorithm for Testing the Sign Stability of an n x n Matrix.

Descriptive Note : Technical rept.,

Corporate Author : WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS

Personal Author(s) : Klee,Victor ; van den Driessche,P.

Report Date : OCT 1975

Pagination or Media Count : 28

Abstract : An n x n real matrix A = (a sub ij) is stable if each eigenvalue has negative real part, and sign stable (or qualitatively stable) if each matrix B having the same sign pattern as A is stable, regardless of the magnitudes of B's entries. Sign stability is of special interest when A is the inter-action matrix of an ecological system, for then the magnitudes of the (a sub ij)'s may be virtually impossible to determine. Starting from a characterization due to Quirk and Ruppert, and to Jeffries, an O(n squared) algorithm is developed for testing the sign stability of A, and when A is properly presented that is reduced to O(max(n, number of nonzero entries of A)). Part of the algorithm is a matching procedure whose extensions are of independent interest. An ALGOL program is included.

Descriptors :   *Matrices(Mathematics), *Computer programming, Computations, Differential equations, Algorithms

Subject Categories : Theoretical Mathematics
      Computer Programming and Software

Distribution Statement : APPROVED FOR PUBLIC RELEASE