Algorithm for the Computation of the Coefficients of Powers of Polynomials.
TEXAS A AND M UNIV COLLEGE STATION
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One of the approaches to determine the global maximum of a multivariate function fx within a feasible region R in the Euclidean n-space is based on the evaluation of the so-called functional moments of fx, that is, the integrals I sub k the integral over R of fx sup kdx for a sequence of integral k. This study is concerned with algorithms accomplishing this task in three special cases. The first case arises when fx is a multivariate polynomial and R is the n dimensional hypercube. In the second case, fx is a multivariate expansion into trigonometric functions and region R is the hypercube. Finally, third case is considered where fx is given by a multivariate polar expansion and R is a smooth convex region in the sense that the distance from an origin in the interior of R to the boundary is a low degree trigonometric expansion in the space angles.
- Operations Research