Estimation of the error in the reduced basis method solution of nonlinear equations

Author:
T. A. Porsching

Journal:
Math. Comp. **45** (1985), 487-496

MSC:
Primary 65H10; Secondary 65G99

MathSciNet review:
804937

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Abstract | References | Similar Articles | Additional Information

Abstract: The reduced basis method is a projection technique for approximating the solution curve of a finite system of nonlinear algebraic equations by the solution curve of a related system that is typically of much lower dimension. In this paper, the reduced basis error is shown to be dominated by an approximation error. This, in turn, leads to error estimates for projection onto specific subspaces; for example, subspaces related to Taylor, Lagrange and discrete least-squares approximation.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1985-0804937-0

Keywords:
Nonlinear equations,
continuation methods,
projection methods

Article copyright:
© Copyright 1985
American Mathematical Society