6533b827fe1ef96bd12863d2

RESEARCH PRODUCT

Quadrature Formula Based on Interpolating Polynomials: Algorithmic and Computational Aspects

Corina SimianDana Simian

subject

Quadrature domainsMathematical analysisGauss–Laguerre quadratureTanh-sinh quadratureGauss–Kronrod quadrature formulaMathematics::Numerical Analysissymbols.namesakesymbolsGauss–Jacobi quadratureGaussian quadratureApplied mathematicsGauss–Hermite quadratureClenshaw–Curtis quadratureMathematics

description

The aim of this article is to obtain a quadrature formula for functions in several variables and to analyze the algorithmic and computational aspects of this formula. The known information about the integrand is {λi(f)}i=1n, where λi are linearly independent linear functionals. We find a form of the coefficients of the quadrature formula which can be easy used in numerical calculations. The main algorithm we use in order to obtain the coefficients and the remainder of the quadrature formula is based on the Gauss elimination by segments method. We obtain an expression for the exactness degree of the quadrature formula. Finally, we analyze some computational aspects of the algorithm in the particular case of the Lagrange conditions.

yearjournalcountryeditionlanguage
2007-05-13
https://doi.org/10.1007/978-3-540-70942-8_50