An O(n squared) Algorithm for Testing the Sign Stability of an n x n Matrix.
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1975
- Accession Number
- ADA018432
Entities
People
- P. Van Den Driessche
- Victor Klee
Organizations
- University of Washington