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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: 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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Keywords: Nonlinear equations, continuation methods, projection methods
Article copyright: © Copyright 1985 American Mathematical Society

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