AN EFFICIENT ALGORITHM FOR THE CLASSICAL LEAST SQUARES APPROXIMATION

Dimitrov, Dimitar K. [UNESP]; Peixoto, Lourenco L.

AN EFFICIENT ALGORITHM FOR THE CLASSICAL LEAST SQUARES APPROXIMATION

Data

2020-01-01

Autores

Dimitrov, Dimitar K.

Peixoto, Lourenco L.

Editor

Siam Publications

Tipo

Artigo

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.