Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Generalized noninterpolatory rules for Cauchy principal value integrals
HTML articles powered by AMS MathViewer

by Philip Rabinowitz PDF
Math. Comp. 54 (1990), 271-279 Request permission

Abstract:

Consider the Cauchy principal value integral \[ I(kf;\lambda ) = \oint k(x)\frac {{f(x)}}{{x - \lambda }} dx,\quad - 1 < \lambda < 1.\] If we approximate $f(x)$ by $\sum _{j = 0}^N\;{a_j}{p_j}(x;w)$ where $\{ {p_j}\}$ is a sequence of orthonormal polynomials with respect to an admissible weight function w and ${a_j} = (f,{p_j})$, then an approximation to $I(kf;\lambda )$ is given by $\sum _{j = 0}^N\;{a_j}I(k{p_j};\lambda )$. If, in turn, we approximate ${a_j}$ by ${a_{jm}} = \sum _{i = 1}^m\;{w_{im}}f({x_{im}}){p_j}({x_{im}})$, then we get a double sequence of approximations $\{ Q_m^N(f;\lambda )\}$ to $I(kf;\lambda )$. We study the convergence of this sequence by relating it to the sequence of approximations associated with $I(wf;\lambda )$ which has been investigated previously.
References
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 65D30
  • Retrieve articles in all journals with MSC: 65D30
Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Math. Comp. 54 (1990), 271-279
  • MSC: Primary 65D30
  • DOI: https://doi.org/10.1090/S0025-5718-1990-0990601-6
  • MathSciNet review: 990601