Error estimates of Gaussian quadrature formulae with the third class of Bernstein-Szegő weights
نویسندگان
چکیده
منابع مشابه
Gaussian Quadrature Formulae for Arbitrary Positive Measures
We present computational methods and subroutines to compute Gaussian quadrature integration formulas for arbitrary positive measures. For expensive integrands that can be factored into well-known forms, Gaussian quadrature schemes allow for efficient evaluation of high-accuracy and -precision numerical integrals, especially compared to general ad hoc schemes. In addition, for certain well-known...
متن کاملOn Multiple Node Gaussian Quadrature Formulae
k Abstract. Let fip . . , Hk be odd positive integers and »i = Z¡=.x(p¡ + 1). Let {«(.}|=j be an extended Tchebycheff system on [a, b]. Let L be a positive linear functional on U = span( {u,}). We prove that L has a unique representation in the form k M,— 1 £<p) = E Z "i/PW(f,). « < h < ■ ■ • < tk < b, 1=1 ;=0 _ k for all p G U. The proof uses the topological degree of a mapping F: D C R k —► R...
متن کاملError Bounds for Gauss-kronrod Quadrature Formulae
The Gauss-Kronrod quadrature formula Qi//+X is used for a practical estimate of the error R^j of an approximate integration using the Gaussian quadrature formula Q% . Studying an often-used theoretical quality measure, for ߣ* , we prove best presently known bounds for the error constants cs(RTMx)= sup \RlK+x[f]\ ll/(l»lloo<l in the case s = "Sn + 2 + tc , k = L^J LfJ • A comparison with the Ga...
متن کاملOn Estimates for the Weights in Gaussian Quadrature in the Ultraspherical Case
In this paper the Christoffel numbers av n for ultraspherical weight functions wk , wx(x) = (\ -x ) ~ ' , are investigated. Using only elementary functions, we state new inequalities, monotonicity properties and asymptotic approximations, which improve several known results. In particular, denoting by dv „ the trigonometric representation of the Gaussian nodes, we obtain for À e [0, 1] the ineq...
متن کاملGaussian interval quadrature rule for exponential weights
Interval quadrature formulae of Gaussian type on R and R+ for exponential weight functions of the form w(x) = exp(−Q(x)), where Q is a continuous function on its domain and such that all algebraic polynomials are integrable with respect to w, are considered. For a given set of nonoverlapping intervals and an arbitrary n, the uniqueness of the n-point interval Gaussian rule is proved. The result...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applicable Analysis and Discrete Mathematics
سال: 2017
ISSN: 1452-8630,2406-100X
DOI: 10.2298/aadm1702451p