Convergence and computation of simultaneous rational quadrature formulas

详细信息    查看全文

• 作者：U. Fidalgo Prieto ; J. R. Illán González and G. López Lagomasino
• 关键词：Mathematics Subject Classification (2000) Primary 41A55 ; Secondary 41A28 ; Secondary 65D32
• 刊名：Numerische Mathematik
• 出版年：2007
• 出版时间：March, 2007
• 年：2007
• 卷：106
• 期：1
• 页码：99-128
• 全文大小：423 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Numerical Analysis
  Mathematics
  Mathematical and Computational Physics
  Mathematical Methods in Physics
  Numerical and Computational Methods
  Applied Mathematics and Computational Methods of Engineering
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：0945-3245

文摘

We discuss the convergence and numerical evaluation of simultaneous quadrature formulas which are exact for rational functions. The problem consists in integrating a single function with respect to different measures using a common set of quadrature nodes. Given a multi-index n, the nodes of the integration rule are the zeros of the multi-orthogonal Hermite–Padé polynomial with respect to (S, α, n), where S is a collection of measures, and α is a polynomial which modifies the measures in S. The theory is based on the connection between Gauss-type simultaneous quadrature formulas of rational type and multipoint Hermite–Padé approximation. The numerical treatment relies on the technique of modifying the integrand by means of a change of variable when it has real poles close to the integration interval. The output of some tests show the power of this approach in comparison with other ones in use.