Control and Estimation of Computational Errors in the Evaluation of Interpolation Formulae and Quadrature Rules

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Abstract
Approximate rules for evaluating linear functionals are often obtained by requiring that the rule shall give exact value for a certain linear class of functions. The parameters of the rule appear hence as the solution of a system of equations. This can generally not be solved exactly but only "numerically." Sometimes large errors occur in the parameters defining the rule, but the resultant error in the computed value of the functional is small. In the present paper we shall develop efficient methods of computing a strict bound for this error in the case when the parameters of the rule are determined from a linear system of equations.

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