منابع مشابه
C∗-algebras and Numerical Linear Algebra
Given a self adjoint operator A on a Hilbert space, suppose that that one wishes to compute the spectrum of A numerically. In practice, these problems often arise in such a way that the matrix of A relative to a natural basis is “sparse”. For example, discretized second order differential operators can be represented by doubly infinite tridiagonal matrices. In these cases it is easy and natural...
متن کاملThe Role of C∗-algebras in Infinite Dimensional Numerical Linear Algebra
This paper deals with mathematical issues relating to the computation of spectra of self adjoint operators on Hilbert spaces. We describe a general method for approximating the spectrum of an operator A using the eigenvalues of large finite dimensional truncations of A. The results of several papers are summarized which imply that the method is effective in most cases of interest. Special atten...
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It is shown that the result of Tso-Wu on the elliptical shape of the numerical range of quadratic operators holds also for the C*-algebra numerical range.
متن کاملNumerical Linear Algebra With
SUMMARY StratiGraph, a Java-based tool for computation and presentation of closure hierarchies of Jordan and Kronecker structures is presented. The tool is based on recent theoretical results on stratiications of orbits and bundles of matrices and matrix pencils. A stratiication reveals the complete hierarchy of nearby structures, information critical for explaining the qualitative behavior of ...
متن کامل“ Numerical Linear Algebra ” course
The main general reference for this and the next two lectures is a recent book [6] and its preliminary version [5] which is freely available on the web. 1 Why iterative methods? As we already know, there are two major classes of methods to solve linear systems: direct methods (like LU factorization, Cholesky factorization, etc.) and iterative methods. We underline the following properties of th...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1994
ISSN: 0022-1236
DOI: 10.1006/jfan.1994.1072