PAT – a Reliable Path-Following Algorithm.

This paper presents a new technique for the reliable computation of the σ-pseudospectrum defined by Λ_σ( A)={ z∈ C : σ_min( A− zI)≤σ} where σ_min is the smallest singular value. The proposed algorithm builds an orbit of adjacent equilateral triangles to capture the level curve ϒ_σ( A)={ z∈ C : σ_min( A− zI)=σ} and uses a bisection procedure on specific triangle vertices to compute a numerical approximation to ϒ_σ. The method is guaranteed to terminate, even in the presence of round-off errors. [ABSTRACT FROM AUTHOR]