A new optimal algorithm for weighted approximation and integration over ℝ

Lei Han, G. W. Wasilkowski

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


The complexities of weighted approximation and weighted integration problems for univariate functions defined over ℝ have recently been found in [7]. Complexity (almost) optimal algorithms have also been provided therein. In this paper, we propose another class of (almost) optimal algorithms that, for a number of instances, are easier to implement. More importantly, these new algorithms have a cost smaller than the original algorithms from [7]. Since both classes of algorithms are (almost) optimal, their costs differ by a multiplicative constant that depends on the specific weight functions and the error demand. In one of our tests we observed this constant to be as large as four, which means a cost reduction by a factor of four.

Original languageEnglish
Pages (from-to)393-406
Number of pages14
JournalNumerical Algorithms
Issue number4
StatePublished - 2000

Bibliographical note

Copyright 2018 Elsevier B.V., All rights reserved.


  • Complexity
  • Optimal algorithms
  • Weighted approximation
  • Weighted integration

ASJC Scopus subject areas

  • Applied Mathematics


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