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Spectral Computations for Bounded Operators (Paperback)
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Spectral Computations for Bounded Operators (Paperback)
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Exact eigenvalues, eigenvectors, and principal vectors of operators
with infinite dimensional ranges can rarely be found. Therefore,
one must approximate such operators by finite rank operators, then
solve the original eigenvalue problem approximately. Serving as
both an outstanding text for graduate students and as a source of
current results for research scientists, Spectral Computations for
Bounded Operators addresses the issue of solving eigenvalue
problems for operators on infinite dimensional spaces. From a
review of classical spectral theory through concrete approximation
techniques to finite dimensional situations that can be implemented
on a computer, this volume illustrates the marriage of pure and
applied mathematics. It contains a variety of recent developments,
including a new type of approximation that encompasses a variety of
approximation methods but is simple to verify in practice. It also
suggests a new stopping criterion for the QR Method and outlines
advances in both the iterative refinement and acceleration
techniques for improving the accuracy of approximations. The
authors illustrate all definitions and results with elementary
examples and include numerous exercises. Spectral Computations for
Bounded Operators thus serves as both an outstanding text for
second-year graduate students and as a source of current results
for research scientists.
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