Algorithm for the computation of the coefficients of powers of polynomials. /
| Main Authors: | , |
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| Corporate Authors: | , |
| Format: | Book |
| Language: | English |
| Published: |
College Station, Texas :
Institute of Statistics, Texas A & M University,
1974.
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| Series: | Technical report (Texas A & M University. Themis Optimization Research Program) ;
no. 49. |
| Subjects: |
| 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. The application of (I sub k) to nonconvex programming is not spelled out in this report but a number of generalizations of the above problem, useful in mathematical programming, are also treated. |
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| Item Description: | "December 1974." "Research conducted through the Texas A & M Research Foundation." This work was also published as the primary author's dissertation to achieve the degree of Ph.D. in Statistics from Texas A & M University. |
| Physical Description: | viii, 76 leaves, 5 unnumbered leaves : illustrations ; 28 cm |
| Bibliography: | Includes bibliographical references (leaves 66-67). |