Lobatto and Radau positive quadrature formulas for linear combinations of Jacobi polynomials

Details Lobatto and Radau positive quadrature formulas for linear combinations of Jacobi polynomials Lobatto and Radau positive quadrature formulas for linear combinations of Jacobi polynomials

2012-04-19

arxiv.org/abs/1204.4473v1

Mathematics

Classical Analysis and ODEs

20 pages

Scientific paper

For a given $\theta\in (-1,1)$, we find out all parameters $\alpha,\beta\in \{0,1\}$ such that, there exists a linear combination of Jacobi polynomials $J_{n+1}^{(\alpha,\beta)}(x)-C J_{n}^{(\alpha,\beta)}(x)$ which generates a Lobatto (Radau) positive quadrature formula of degree of exactness \textcolor{red}{$2n+2$ ($2n+1$)} and contains the point $\theta$ as a node. These positive quadratures are very useful in studying problems in one-sided polynomial $L_1$ approximation.

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