This paper presents a new technique for the reliable computation of the s-pseudospectrum defined by ?s(A)={z?C : smin(A-zI)=s} where smin is the smallest singular value. The proposed algorithm builds an orbit of adjacent equilateral triangles to capture the level curve ?s(A)={z?C : smin(A-zI)=s} and uses a bisection procedure on specific triangle vertices to compute a numerical approximation to ?s. The
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