Algorithm for the Computation of the Coefficients of Powers of Polynomials.
Abstract
One of the approaches to determine the global maximum of a multivariate function f(x) within a 'feasible region' R in the Euclidean n-space is based on the evaluation of the so-called functional moments of f(x), that is, the integrals (I sub k) = the integral over R of f(x) (sup k)dx for a sequence of integral k. This study is concerned with algorithms accomplishing this task in three special cases. The first case arises when f(x) is a multivariate polynomial and R is the n dimensional hypercube. In the second case, f(x) is a multivariate expansion into trigonometric functions and region R is the hypercube. Finally, third case is considered where f(x) 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1974
- Accession Number
- ADA003594
Entities
People
- Genyu Chen
- Herman Otto Hartley
Organizations
- Texas A&M University