Error estimates of anti-Gaussian quadrature formulae

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

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 کامل

On 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 کامل

Anti-Gaussian quadrature formulas

An anti-Gaussian quadrature formula is an (n+ 1)-point formula of degree 2n− 1 which integrates polynomials of degree up to 2n+ 1 with an error equal in magnitude but of opposite sign to that of the n-point Gaussian formula. Its intended application is to estimate the error incurred in Gaussian integration by halving the difference between the results obtained from the two formulas. We show tha...

متن کامل

Error 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 کامل

Nonstandard Gaussian quadrature formulae based on operator values

In this paper, we develop the theory of so-called nonstandard Gaussian quadrature formulae based on operator values for a general family of linear operators, acting of the space of algebraic polynomials, such that the degrees of polynomials are preserved. Also, we propose a stable numerical algorithm for constructing such quadrature formulae. In particular, for some special classes of linear op...

متن کامل

ذخیره 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: Journal of Computational and Applied Mathematics

سال: 2012

ISSN: 0377-0427

DOI: 10.1016/j.cam.2011.03.026