On computational applications of the theory of moment problems
Sven-Åke Gustafson · Rocky Mountain Journal of Mathematics · 1974
Many computational problems can be formulated as the task to evaluate a linear functional L for a given function <P when L is subject to a finite number of constraints.In this paper we discuss tasks of this form.L(<P) can be evaluated numerically either by approximating *P with linear combinations of a given system of functions u\ 9 1*2, **•, u n or by approximating L with a finite sum.In this way one can treat effectively such problems as the evaluation of a class of slowly convergent Fourier integrals, finding the limit value of sequences and the approximation of functions.In our theoretical analysis we shall use the theory of the moment problem and consider generalizations of an optimization problem first studied by A. A. Markov and P. L. Cebysev.We extend the results in various directions using the theory of semi-infinite programming.