Spectral Methods for Parameterized Matrix Equations

Details Spectral Methods for Parameterized Matrix Equations Spectral Methods for Parameterized Matrix Equations

2009-04-14

arxiv.org/abs/0904.2040v1

SIAM. J. Matrix Anal. & Appl. 31, pp. 2681-2699, 2010

Mathematics

Numerical Analysis

18 pages, 2 figures, 1 table

Scientific paper

10.1137/090755965

We apply polynomial approximation methods -- known in the numerical PDEs context as spectral methods -- to approximate the vector-valued function that satisfies a linear system of equations where the matrix and the right hand side depend on a parameter. We derive both an interpolatory pseudospectral method and a residual-minimizing Galerkin method, and we show how each can be interpreted as solving a truncated infinite system of equations; the difference between the two methods lies in where the truncation occurs. Using classical theory, we derive asymptotic error estimates related to the region of analyticity of the solution, and we present a practical residual error estimate. We verify the results with two numerical examples.

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