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A note on computation of pseudospectra. (English) Zbl 1255.65078

Summary: The aim is to contribute to pseudospectra computation via a path following technique. Given a matrix \(A \in \mathbb C^{n \times n}\), we compute the branch consisting of a fixed singular value \(\varepsilon \) and corresponding left and right singular vectors of the parameter dependent matrix \((x + iy)I - A\). The fact that the branch corresponds to the smallest singular value \(\sigma _{\min}((x + iy)I - A) = \epsilon \) is sufficient to verify at just one point of the branch due to the continuity argument. We can exploit a standard ready-made software.

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15A18 Eigenvalues, singular values, and eigenvectors
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