Calculation of Gauss quadrature rules.
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Cites background from "Calculation of Gauss quadrature rul..."
...Note that we do not need to form the polynomial and then compute its roots, but instead it is numerically more stable to compute the roots as eigenvalues of a suitable tridiagonal matrix (Golub and Welsch, 1969)....
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Cites background or methods from "Calculation of Gauss quadrature rul..."
...Gauss quadrature nodes and weights take more work to calculate, but this can be done with excellent accuracy in O(n3) operations by solving a tridiagonal eigenvalue problem, as shown by Golub and Welsch [22]....
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...For example, Stroud and Secrest worked in multiple precision and before the days of Golub and Welsch [31]; meanwhile gauss....
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...Their impact was mainly theoretical before the advent of computers, because of the difficulty of determining the nodes and weights and also of evaluating integrands at irrational arguments, but in the computer era, especially since the appearance of a paper by Golub and Welsch in 1969 (following earlier work of Goertzel in 1954, Wilf in 1962, and Gordon in 1968), it has been practical as well [31]....
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...operations by solving a tridiagonal eigenvalue problem, as shown by Golub and Welsch [31]....
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...Their impact was mainly theoretical before the advent of computers, because of the difficulty of determining the nodes and weights and also of evaluating integrands at irrational arguments, but in the computer era, especially since the appearance of a paper by Golub and Welsch in 1969 (following earlier work of Goertzel 1954, Wilf 1962 and Gordon 1968), it has been practical as well [22]....
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