In this paper an accurate method to construct the bidiagonal factorization of collocation and Wronskian matrices of Jacobi polynomials is obtained and used to compute with high relative accuracy their eigenvalues, singular values and inverses. The particular cases of collocation and Wronskian matrices of Legendre polynomials, Gegenbauer polynomials, Chebyshev polynomials of the first and second kind and rational Jacobi polynomials are considered. Numerical examples are included.

中文翻译：

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Jacobi多项式的搭配和Wronskian矩阵的精确计算

本文获得了一种构造Jacobi多项式的配位和Wronskian矩阵的对角分解的准确方法，并以较高的相对精度计算了它们的特征值，奇异值和逆。考虑了第一类和第二类Legendre多项式，Gegenbauer多项式，Chebyshev多项式以及有理Jacobi多项式的搭配和Wronskian矩阵的特殊情况。包括数值示例。