Construction of Gaussian quadrature formulas for even weight functions

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

Numerical Construction of Gaussian Quadrature Formulas for

Most nonclassical Gaussian quadrature rules are difficult to construct because of the loss of significant digits during the generation of the associated orthogonal polynomials. But, in some particular cases, it is possible to develop stable algorithms. This is true for at least two well-known integrals, namely ¡l-(Loêx)-x°f(x)dx and ¡Ô Em(x)f(x)-dx. A new approach is presented, which makes use ...

متن کامل

On the Remainder of Gaussian Quadrature Formulas for Bernstein-szegö Weight Functions

We give an explicit expression for the kernel of the error functional for Gaussian quadrature formulas with respect to weight functions of BernsteinSzegö type, i.e., weight functions of the form (1 x)"(l + x)ß /p(x), x e (-1, 1), where a, ß £ {-\,\} and p is a polynomial of arbitrary degree which is positive on [-1, 1]. With the help of this result the norm of the error functional can easily be...

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

Construction of σ-orthogonal Polynomials and Gaussian Quadrature Formulas

Let dα be a measure on R and let σ = (m1,m2, ..., mn), where mk ≥ 1, k = 1, 2, ..., n, are arbitrary real numbers. A polynomial ωn(x) := (x − x1)(x − x2)...(x − xn) with x1 ≤ x2 ≤ ... ≤ xn is said to be the n-th σ-orthogonal polynomial with respect to dα if the vector of zeros (x1, x2, ..., xn) is a solution of the extremal problem ∫

متن کامل

Szegö quadrature formulas for certain Jacobi-type weight functions

In this paper we are concerned with the estimation of integrals on the unit circle of the form ∫ 2π 0 f(eiθ)ω(θ)dθ by means of the so-called Szegö quadrature formulas, i.e., formulas of the type ∑n j=1 λjf(xj) with distinct nodes on the unit circle, exactly integrating Laurent polynomials in subspaces of dimension as high as possible. When considering certain weight functions ω(θ) related to th...

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: Applicable Analysis and Discrete Mathematics

سال: 2017

ISSN: 1452-8630,2406-100X

DOI: 10.2298/aadm1701177m