Приказ основних података о документу
Error bounds for Gauss-type quadratures with Bernstein-Szego weights
dc.creator | Pejčev, Aleksandar | |
dc.date.accessioned | 2022-09-19T17:23:59Z | |
dc.date.available | 2022-09-19T17:23:59Z | |
dc.date.issued | 2014 | |
dc.identifier.issn | 1017-1398 | |
dc.identifier.uri | https://machinery.mas.bg.ac.rs/handle/123456789/1884 | |
dc.description.abstract | The paper is concerned with the derivation of error bounds for Gauss-type quadratures with Bernstein-Szego weights, integral(1)(-1) f(t)w(t) dt = G(n)[f] + R-n(f), G(n)[f] = Sigma(n)(nu=1) lambda(nu)f(tau(nu)) (n is an element of N), where f is an analytic function inside an elliptical contour epsilon(rho) with foci at -/+ 1 and sum of semi-axes rho > 1, and w is a nonnegative and integrable weight function of Bernstein-Szego type. The derivation of effective bounds on vertical bar R-n(f)vertical bar is possible if good estimates of max(z is an element of epsilon rho) vertical bar K-n(z)vertical bar are available, especially if one knows the location of the extremal point eta is an element of epsilon(rho) at which vertical bar K-n vertical bar attains its maximum. In such a case, instead of looking for upper bounds on max(z is an element of epsilon rho) vertical bar K-n(z)vertical bar, one can simply try to calculate vertical bar Kn(eta, w)vertical bar. In the case under consideration, i.e. when w(t) = (1 - t(2))(-1/2)/beta(beta - 2 alpha)t(2) + 2 delta(beta - alpha)t + alpha(2) + delta(2), t is an element of (-1, 1), for some alpha, beta, delta, which satisfy 0 lt alpha lt beta, beta not equal 2 alpha, vertical bar delta vertical bar lt beta - alpha, the location on the elliptical contours where the modulus of the kernel attains its maximum value is investigated. This leads to effective bounds on vertical bar R-n(f)vertical bar. The quality of the derived bounds is analyzed by a comparison with other error bounds proposed in the literature for the same class of integrands. | en |
dc.publisher | Springer, Dordrecht | |
dc.relation | info:eu-repo/grantAgreement/MESTD/Basic Research (BR or ON)/174002/RS// | |
dc.rights | restrictedAccess | |
dc.source | Numerical Algorithms | |
dc.subject | Remainder term | en |
dc.subject | Kernel | en |
dc.subject | Gaussian quadrature | en |
dc.subject | Error bound | en |
dc.subject | Elliptical contour | en |
dc.subject | Analytic function | en |
dc.title | Error bounds for Gauss-type quadratures with Bernstein-Szego weights | en |
dc.type | article | |
dc.rights.license | ARR | |
dc.citation.epage | 590 | |
dc.citation.issue | 3 | |
dc.citation.other | 66(3): 569-590 | |
dc.citation.rank | M21 | |
dc.citation.spage | 569 | |
dc.citation.volume | 66 | |
dc.identifier.doi | 10.1007/s11075-013-9749-0 | |
dc.identifier.scopus | 2-s2.0-84903478361 | |
dc.identifier.wos | 000338336900008 | |
dc.type.version | publishedVersion |