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Applied and computational Analysis Seminars

Spectral inclusions and approximations of finite and infinite banded matrices

With Marko Lindner

Spectral inclusions and approximations of finite and infinite banded matrices

We derive inclusion sets and approximations to spectrum and pseudospectrum of banded, in general non-normal, matrices of finite or infinite size. In the infinite case (bi- or semi-infinite), the matrix acts as a bounded linear operator on the corresponding l^2 space, and we moreover bound and approximate its essential spectrum.

Our inclusion sets come as unions of pseudospectra of certain submatrices of chosen size. Via this choice, we can balance accuracy against numerical cost. The philosophy is to split one global spectral problem into several local problems of moderate size.

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