Nonequivalence deflation for the solution of matrix latent value problems

The following nonlinear latent value problem is studied: F(λ)x = 0, where F(λ) is an n × n analytic nondefective matrix function in the scalar λ. The latent pair (λ, x) has been previously found by applying Newton's method to a certain equation. The deflation technique is required for finding another latent pair starting from a computed latent pair. Several deflation strategies are examined, and the nonequivalence deflation technique is developed. It is demonstrated, by analysis and numerical experience, to be a reliable and efficient strategy for finding a few latent roots in a given region.