AF embeddings and the numerical computation of spectra in irrational rotation algebras

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Abstract

A natural problem at the interface of operator theory and numerical analysis is that of finding a (finite dimensional) matrix whose eigenvalues approximate the spectrum of a given (infinite dimensional) operator. It is well-known that classical work of Pimsner and Voiculescu produces explicit matrix models for an interesting class of nontrivial examples (e.g., many discretized one-dimensional Schrödinger operators). In this paper, we observe that the spectra of their models (often) converge in the strongest possible sense - in the Hausdorff metric - and demonstrate that the rate of convergence is, in general, best possible.

Original languageEnglish (US)
Pages (from-to)517-528
Number of pages12
JournalNumerical Functional Analysis and Optimization
Volume27
Issue number5-6
DOIs
StatePublished - Sep 1 2006

All Science Journal Classification (ASJC) codes

  • Analysis
  • Signal Processing
  • Computer Science Applications
  • Control and Optimization

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