## Abstract

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 language | English |
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Pages (from-to) | 393-406 |

Number of pages | 14 |

Journal | Numerical Algorithms |

Volume | 23 |

Issue number | 4 |

DOIs | |

State | Published - 2000 |

### Bibliographical note

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

## Keywords

- Complexity
- Optimal algorithms
- Weighted approximation
- Weighted integration

## ASJC Scopus subject areas

- Applied Mathematics