On the optimum choice of weight functions in a class of variational calculations |
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| Authors: | Prof Dr L M Delves Dr M Bain |
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| Institution: | (1) Dept. of Computational and Statistical Science, University of Liverpool, Victoria Building, Brownlow Hill, PO Box 147, L69 3BX Liverpool, England;(2) The Computer Laboratory, University of Leicester, LE 1 7RH Leicester, England |
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| Abstract: | Summary We consider the variational solution of a particular class of second order differential equations and show that expansions in terms of Chebychev and a range of ultraspherical polynomials lead to operator matrices that are asymptotically diagonal, and that hence their convergence properties can be completely characterised using a previously developed analysis. For a given class of weight functions bounds are given on the convergence of the coefficients and of the weighted mean square error, in terms of the analyticity properties of the coefficients in the differential equation. These bounds are used to discuss the optimum choice of weight function for such a calculation. |
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