A fast algorithm for generalized Hankel matrices arising in finite-moment problems
✍ Scribed by Luca Gemignani
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 502 KB
- Volume
- 267
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
✦ Synopsis
Consider an n X n lower triangular matrix L whose (i + l)st row is defined by the coefficients of the real polynomial pi(x) of degree i such that {p,(x)} is's set of orthogonal polynomials satisfying a standard three-term recurrence relation. If H is an n X n real Hankel matrix with nonsingular leading principal submatrices, then P? = LHLT will be referred to as a strongly nonsingular Hankel matrix with respect to the orthogonal polynomial basis {p,(r)}. In this paper we develop an efficient O(n") algorithm for the splution of a system of linear equations with a real symmetric coefficient matrix H which is a Hankel matrix with respect to a suitable orthogonal polynomial basis. This leads to an efficient method for computing polynomial approximations of an unknown function given its modified moments.