APPROXIMATE CALCULATION OF SUMS I: BOUNDS FOR THE ZEROS OF GRAM POLYNOMIALS
Contribuinte(s) |
Universidade Estadual Paulista (UNESP) |
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Data(s) |
18/03/2015
18/03/2015
01/01/2014
|
Resumo |
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Processo FAPESP: 09/13832-9 Processo FAPESP: 13/23606-1 Let N be a positive integer and x(j) be N equidistant points. We propose an algorithmic approach for approximate calculation of sums of the form Sigma(N)(j=1) F(x(j)). The method is based on the Gaussian type quadrature formula for sums, Sigma F-N(j =1)(x(j)) approximate to Sigma B-n(k=1)n,k F(g(n,k)(N)), n << N,where g(n,k)(N) are the zeros of the so-called Gram polynomials. This allows the calculation of sums with very large number of terms N to be reduced to sums with a much smaller number of summands n. The first task in constructing such a formula is to calculate its nodes g(n,k)(N). In this paper we obtain precise lower and upper bounds for g(n,k)(N). Numerical experiments show that the estimates for the zeros g(n,k)(N) are very sharp and that the proposed method for calculation of sums is efficient. |
Formato |
1867-1886 |
Identificador |
http://dx.doi.org/10.1137/120887278 Siam Journal On Numerical Analysis. Philadelphia: Siam Publications, v. 52, n. 4, p. 1867-1886, 2014. 0036-1429 http://hdl.handle.net/11449/117189 10.1137/120887278 WOS:000341571300005 |
Idioma(s) |
eng |
Publicador |
Siam Publications |
Relação |
Siam Journal On Numerical Analysis |
Direitos |
closedAccess |
Palavras-Chave | #approximate calculation of sums #Gaussian type quadrature formula for sums #orthogonal Gram polynomials #zeros of Gram polynomials |
Tipo |
info:eu-repo/semantics/article |