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

DOI:
https://doi.org/10.1090/S0025-5718-1988-0942144-4

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 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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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1988-0942144-4

Keywords:
Least squares solutions,
regularization,
ill-posed problems,
asymptotic expansions for discretization,
Richardson extrapolation

Article copyright:
© Copyright 1988
American Mathematical Society