On the approximation of spectra of linear operators on Hilbert spaces

By Anders Christian Hansen. 2008

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Abstract We present several new techniques for approximating spectra of linear operators (not necessarily bounded) on an infinite-dimensional, separable Hilbert space. Our approach is to take well-known techniques from finite-dimensional matrix analysis and show how they can be generalized to an infinite-dimensional setting to provide approximations of spectra of elements in a large class of operators. We conclude by proposing a solution to the general problem of approximating the spectrum of an arbitrary bounded operator by introducing the n -pseudospectrum and argue how that can be used as an approximation to the spectrum.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7dda0f42a856eb7a6418a9bc4823155c904d6f21