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Mathematics of Computation

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Asymptotic expansions for the discretization error of least squares solutions of linear boundary value problems

Authors: Klaus Böhmer and John Locker
Journal: Math. Comp. 51 (1988), 75-91
MSC: Primary 65L10
MathSciNet review: 942144
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Abstract: For determining least squares solutions of linear boundary value problems, the method of regularization provides uniquely solvable boundary value problems, which are solved with difference methods. The determination of the coefficients in an asymptotic expansion of the discretization error in powers of the regularization and discretization parameters $\alpha$ and h, respectively, is an ill-posed problem. We present here an asymptotic expansion of this type and discuss the numerical implications for Richardson extrapolation, thereby establishing for the first time methods of arbitrarily high order.

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Keywords: Least squares solutions, regularization, ill-posed problems, asymptotic expansions for discretization, Richardson extrapolation
Article copyright: © Copyright 1988 American Mathematical Society