### Abstract

In this paper and two companion papers, we produce efficient algorithms to solve the following interpolation problem: Let m ≥ 1 and p > n ≥ 1. Given a finite set E C Rn and a function f : E → R, compute an extension F of f belonging to the Sobolev space Wm,p(Rn) with norm having the smallest possible order of magnitude; secondly, compute the order of magnitude of the norm of F. The combined running time of our algorithms is at most CNlogN, where N denotes the cardinality of E, and C depends only on m, n, and p.

Original language | English (US) |
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Pages (from-to) | 1039-1126 |

Number of pages | 88 |

Journal | Revista Matematica Iberoamericana |

Volume | 32 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2016 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Keywords

- Algorithm
- Interpolation
- Sobolev spaces

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## Cite this

Fefferman, C., Israel, A., & Luli, G. K. (2016). Fitting a Sobolev function to data III.

*Revista Matematica Iberoamericana*,*32*(3), 1039-1126. https://doi.org/10.4171/rmi/908