Name
Abstract | ||
|---|---|---|
Let H∞,βr˜, denote those 2π-periodic, real-valued functions f on R, which are analytic in the strip Sβ:= {z ∈ C: |Im z| 0 and satisfy the restriction |f(r)(z)| ≤1, z ∈ Sβ. Denote by [x] the integral part of x. We prove that the rectangular formula QN*(f) = 2π/N Σj=0N-1 f(2πj/N) is optimal for the class of functions H∞,βr˜ among all quadrature formulae of the form Q2N(f) = Σi=1n Σj=0vi-1 aijf(j)(ti), where the nodes 0 ≤ t1 tn aij ∈ R are arbitrary, i = 1,...,n, j = 0, 1,..., vi - 1, and (v1,...,vn) is a system of positive integers satisfying the condition Σi=1n 2[(vi + 1)/2] ≤ 2N. In particular, the rectangular formula is optimal for the class of functions H∞,βr˜ among all quadrature formulae of the form: QN(f) = Σi=1N aif(ti), where 0≤t1 tN ai ∈ R, i = 1,...,N. Moreover, we exactly determine the error estimate of the optimal quadrature formulae on the class H∞,βr˜ |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1016/j.jco.2005.01.002 | J. Complexity |
Keywords | DocType | Volume |
hardy-sobolev classes,optimal quadrature formula,analytic function,error estimate,functions H,t1 tN,quadrature formula,class H,Sobolev class,Hardy-Sobolev class,real-valued function,form Q2N,t1 tn aij,optimal quadrature problem,integral part,rectangular formula | Journal | 21 |
Issue | ISSN | Citations |
5 | Journal of Complexity | 2 |
PageRank | References | Authors |
0.52 | 2 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| FANG GENSUN | 1 | 26 | 8.25 |
| Xuehua Li | 2 | 100 | 10.07 |