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Please use this identifier to cite or link to this item: http://acervodigital.unesp.br/handle/11449/117189
Title: 
APPROXIMATE CALCULATION OF SUMS I: BOUNDS FOR THE ZEROS OF GRAM POLYNOMIALS
Author(s): 
Institution: 
  • Univ Vigo
  • Universidade Estadual Paulista (UNESP)
  • Universidade Federal de São Paulo (UNIFESP)
ISSN: 
0036-1429
Sponsorship: 
  • Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
  • Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
  • Ministerio de Ciencia e Innovacion of Spain - European Community fund FEDER
Sponsorship Process Number: 
  • CNPq: 307183/2013-0
  • FAPESP: 09/13832-9
  • FAPESP: 13/23606-1
  • Ministerio de Ciencia e Innovacion of Spain - European Community fund FEDERMTM2009-14668-C02-01
  • Ministerio de Ciencia e Innovacion of Spain - European Community fund FEDERMTM2012-38794-C02-01
Abstract: 
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.
Issue Date: 
1-Jan-2014
Citation: 
Siam Journal On Numerical Analysis. Philadelphia: Siam Publications, v. 52, n. 4, p. 1867-1886, 2014.
Time Duration: 
1867-1886
Publisher: 
Siam Publications
Keywords: 
  • approximate calculation of sums
  • Gaussian type quadrature formula for sums
  • orthogonal Gram polynomials
  • zeros of Gram polynomials
Source: 
http://dx.doi.org/10.1137/120887278
URI: 
Access Rights: 
Acesso restrito
Type: 
outro
Source:
http://repositorio.unesp.br/handle/11449/117189
Appears in Collections:Artigos, TCCs, Teses e Dissertações da Unesp

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