Computation of Gauss-type quadrature formulas
نویسندگان
چکیده
منابع مشابه
On computing rational Gauss-Chebyshev quadrature formulas
We provide an algorithm to compute the nodes and weights for Gauss-Chebyshev quadrature formulas integrating exactly in spaces of rational functions with arbitrary real poles outside [−1, 1]. Contrary to existing rational quadrature formulas, the computational effort is very low, even for extremely high degrees, and under certain conditions on the poles it can be shown that the complexity is of...
متن کاملComputation of Gauss-Kronrod quadrature rules
Recently Laurie presented a new algorithm for the computation of (2n+1)-point Gauss-Kronrod quadrature rules with real nodes and positive weights. This algorithm first determines a symmetric tridiagonal matrix of order 2n+ 1 from certain mixed moments, and then computes a partial spectral factorization. We describe a new algorithm that does not require the entries of the tridiagonal matrix to b...
متن کاملConstruction of Gauss-Christ of fei Quadrature Formulas
Each of these rules will be called a Gauss-Christoffel quadrature formula if it has maximum degree of exactness, i.e. if (1.1) is an exact equality whenever / is a polynomial of degree 2n — 1. It is a well-known fact, due to Christoffel [3], that such quadrature formulas exist uniquely, provided the weight function w(x) is nonnegative, integrable with /* w(x)dx > 0, and such that all its moments
متن کاملStieltjes Polynomials and the Error of Gauss-kronrod Quadrature Formulas
The Gauss-Kronrod quadrature scheme, which is based on the zeros of Legendre polynomials and Stieltjes polynomials, is the standard method for automatic numerical integration in mathematical software libraries. For a long time, very little was known about the error of the Gauss-Kronrod scheme. An essential progress was made only recently, based on new bounds and as-ymptotic properties for the S...
متن کاملError of the Newton-Cotes and Gauss-Legendre Quadrature Formulas
Abstract. It was shown by P. J. Davis that the Newton-Cotes quadrature formula is convergent if the integrand is an analytic function that is regular in a sufficiently large region of the complex plane containing the interval of integration. In the present paper, a bound on the error of the Newton-Cotes quadrature formula for analytic functions is derived. Also the bounds on the Legendre polyno...
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: Journal of Computational and Applied Mathematics
سال: 2001
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(00)00506-9