AN EFFICIENT ALGORITHM FOR THE CLASSICAL LEAST SQUARES APPROXIMATION

Autor(es)

Dimitrov, Dimitar K. ^[1] ; Peixoto, Lourenco L. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Paulista, Dept Matemat, IBILCE, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

^[2] Inst Fed Minas Gerais, Dept Matemat, BR-36415000 Congonhas, MG - Brazil

• Tipo de documento: Artigo Científico
• Fonte: SIAM JOURNAL ON SCIENTIFIC COMPUTING; v. 42, n. 5, p. A3233-A3249, 2020.
• Citações Web of Science: 0

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. (AU)

• Processo FAPESP: 16/09906-0 - Análise harmônica, teoria da aproximação, funções especiais e aplicações
• Beneficiário: Dimitar Kolev Dimitrov
• Modalidade de apoio: Auxílio à Pesquisa - Temático