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Mathematics of Computation

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Quasi-diagonality and the finite section method

Author: Nathanial P. Brown
Journal: Math. Comp. 76 (2007), 339-360
MSC (2000): Primary 65J10, 46N40
Published electronically: August 31, 2006
MathSciNet review: 2261025
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Abstract: Quasi-diagonal operators on a Hilbert space are a large and important class (containing all self-adjoint operators for instance). They are also perfectly suited for study via the finite section method (a particular Galerkin method). Indeed, the very definition of quasi-diagonality yields finite sections with good convergence properties. Moreover, simple operator theory techniques yield estimates on certain rates of convergence. In the case of quasi-diagonal band operators both the finite sections and rates of convergence are explicitly given.

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Additional Information

Nathanial P. Brown
Affiliation: Department of Mathematics, Penn State University, State College, Pennsylvania 16802

Received by editor(s): February 16, 2005
Received by editor(s) in revised form: November 9, 2005
Published electronically: August 31, 2006
Additional Notes: The work of this author was partially supported by an NSF Postdoctoral Fellowship and DMS-0244807.
Article copyright: © Copyright 2006 American Mathematical Society

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