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

1985/01/01 by T. A. Porsching · 7 citations
Engineering · Computer Science · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Matrix Theory and Algorithms #Model Reduction and Neural Networks

paper · pdf · doi:10.1090/s0025-5718-1985-0804937-0

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.

Citations

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