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Computation of matrix pseudospectra by exclusion regions and remotion pane. (Chinese. English summary) Zbl 1125.65126

Summary: The standard grid method (GRID), which is traditionally used to accurately compute the \(\varepsilon\)-pseudospectrum \(\Lambda\varepsilon(A)\) of a matrix \(A\), is a process of highly demanding computational tasks. At each point of domain of interest, the GRID computes \(\varepsilon_{min}(zI-A)\) and uses that information in order to classify the point as belonging to \(\Lambda\varepsilon(A)\) or not. It means that we shall pay much time for the computation at those points out of the curve. In this paper, we provide two new methods to compute pseudospectra: exclusion regions and remotion pane. They could shrink the regions remarkably and accelerate the speed of computational process. Numerical experiments further show the effectiveness of the methods reported here.

MSC:

65Y20 Complexity and performance of numerical algorithms
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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