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arXiv · 2412.20849

Gaussian Quadratures with prescribed nodes via moment theory

Rajkamal Nailwal·Aljaž Zalar
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Abstract

Let $\mu$ be a positive Borel measure on the real line and let $L$ be the linear functional on univariate polynomials of bounded degree, defined as integration with respect to $\mu$. In 2020, Blekherman et al., the characterization of all minimal quadrature rules of $\mu$ in terms of the roots of a bivariate polynomial is given and two determinantal representations of this polynomial are established. In particular, the authors solved the question of the existence of a minimal quadrature rule with one prescribed node, leaving open the extension to more prescribed nodes. In this paper, we solve this problem using moment theory as the main tool.

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Rajkamal Nailwal, Aljaž Zalar. 2024-12-30. Gaussian Quadratures with prescribed nodes via moment theory. https://arxiv.org/abs/2412.20849

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