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 ⊆ 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) | 275-376 |
Number of pages | 102 |
Journal | Revista Matematica Iberoamericana |
Volume | 32 |
Issue number | 1 |
DOIs | |
State | Published - 2016 |
All Science Journal Classification (ASJC) codes
- General Mathematics
Keywords
- Algorithm
- Interpolation
- Sobolev spaces