Summary
Algorithms are derived for the evaluation of Gauss knots in the presence of fixed knots by modification of the Jacobi matrix for the weight function of the integral. Simple Gauss knots are obtained as eigenvalues of symmetric tridiagonal matrices and a rapidly converging simple iterative process, based on the merging of free and fixed knots, of quadratic convergence is presented for multiple Gauss knots. The procedures also allow for the evaluation of the weights of the quadrature corresponding to the simple Gauss knots. A new characterization of simple Gauss knots as a solution of a partial inverse eigenvalue problem is derived.
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Supported in part by the United States Department of Energy contract DE-AT-03-ER71030 and in part by the National Science Foundation grant MCS-78-11985
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Golub, G.H., Kautsky, J. Calculation of Gauss quadratures with multiple free and fixed knots. Numer. Math. 41, 147–163 (1983). https://doi.org/10.1007/BF01390210
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DOI: https://doi.org/10.1007/BF01390210