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AN EFFICIENT ALGORITHM FOR THE CLASSICAL LEAST SQUARES APPROXIMATION
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DOI：10.1137/19M1259936.png)
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Abstract
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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.
Keywords:
least squares approximation
Gaussian quadrature
orthogonal Gram polynomials
WDDK method
Newton-Raphson method
Golub-Welsch algorithm
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