## Abstract

The paper considers linear problems on weighted spaces of multivariate functions of many variables. The main questions addressed are the following: when is it possible to approximate the solution for the original function of very many variables by the solution for the same function, however with all but the first k variables set to zero, so that the corresponding error is small? What is the truncation dimension, i.e., the smallest number k = k(ε) such that the corresponding error is bounded by a given error demand ε? Surprisingly, k(ε) could be very small even for weights with a modest speed of convergence to zero.

Original language | English |
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Pages (from-to) | 661-685 |

Number of pages | 25 |

Journal | Numerical Algorithms |

Volume | 80 |

Issue number | 2 |

DOIs | |

State | Published - Feb 6 2019 |

### Bibliographical note

Publisher Copyright:© 2018, Springer Science+Business Media, LLC, part of Springer Nature.

## Keywords

- Multivariate problems
- Truncation algorithms
- Truncation dimension
- Weighted function spaces

## ASJC Scopus subject areas

- Applied Mathematics