Asymptotic expansions for the discretization error of least squares solutions of linear boundary value problems
Klaus Böhmer, John Locker · Mathematics of Computation · 1988
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 α \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.