Testing eigenvalue software.

Abstract

This dissertation describes a significant advance in automated testing of eigenvalue software. Several programs are described that assist the researcher in verifying that a new program is stable. Using backwards error techniques popularized by Wilkinson, a maximizer or "hill climber" systematically searches for instabilities in the program being tested. This work builds on software first reported by Miller and removes the restriction of not being able to work on iterative methods. Testing eigenvalue solver programs with sets of small random input data can often find instabilities, but the described hill climbing technique is more efficient. Using only ten sets of starting points, the maximizer will often find the instability, if it exists, in only a few tries.