AN EFFICIENT ALGORITHM FOR THE CLASSICAL LEAST SQUARES APPROXIMATION
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Siam Publications
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Resumo
We explore the computational issues concerning a new algorithm for the classical least-squares approximation of N samples by an algebraic polynomial of degree at most n when the number N of the samples is very large. The algorithm is based on a recent idea about accurate numerical approximations of sums with large numbers of terms. For a fixed n, the complexity of our algorithm in double precision accuracy is O(1). It is faster and more precise than the standard algorithm in MATLAB.
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least squares approximation, Gaussian quadrature, orthogonal Gram polynomials, WDDK method, Newton-Raphson method, Golub-Welsch algorithm
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Inglês
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Siam Journal On Scientific Computing. Philadelphia: Siam Publications, v. 42, n. 5, p. A3233-A3249, 2020.
