Gaussian interval quadrature rule for exponential weights

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• 作者：Aleksandar S. Cvetkovi膰^a ; ^{aleksandarcvetkovic@pmf.ni.ac.rs} ; Gradimir V. Milovanovi膰^b ; ^{gvm@mi.sanu.ac.rs}
• 关键词：Exponential weight ; Numerical integration ; Interval quadrature rule ; Weight coefficients ; Nodes
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：15 May, 2012
• 卷：218
• 期：18
• 页码：9332-9341
• 文件大小：223 K

摘要

Interval quadrature formulae of Gaussian type on and for exponential weight functions of the form m>wm>(m>xm>) = exp(鈭?em>Qm>(m>xm>)), where m>Qm> is a continuous function on its domain and such that all algebraic polynomials are integrable with respect to m>wm>, are considered. For a given set of nonoverlapping intervals and an arbitrary m>nm>, the uniqueness of the m>nm>-point interval Gaussian rule is proved. The results can be applied also to corresponding quadratures over (鈭?, 1). An algorithm for the numerical construction of interval quadratures is presented. Finally, in order to illustrate the presented method, two numerical examples are done.