PAT -- a reliable path-following algorithm (Q5961059)

The paper presents a new technique intended for reliable computation of the pseudospectrum of a matrix at a low cost. The algorithm proposed may be considered as a specialization of the piecewise-linear methods for the pseudospectrum problem. It builds an orbit of adjacent equilateral triangles to capture the level curve and uses a bisection procedure on specific triangle vertices to compute a numerical approximation to the curve. A forward error analysis is presented which shows that the method is guaranteed to terminate, even in the presence of round-off errors. An example with a matrix of order 100, which is ill-conditioned with respect to its eigensystem, is presented. The results demonstrate that the proposed algorithm copes easily with directional discontinuities along the level curve.