Structure-Preserving Function Approximation via Convex Optimization
| Autor: | Vidhi Zala, Akil Narayan, Michael Kirby |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Polynomial
Approximations of π Applied Mathematics 010102 general mathematics Structure (category theory) Numerical Analysis (math.NA) 010103 numerical & computational mathematics Function (mathematics) 01 natural sciences Computational Mathematics Function approximation 41A29 65D15 65K05 90C25 42A16 Optimization and Control (math.OC) Convex optimization FOS: Mathematics Applied mathematics Mathematics - Numerical Analysis 0101 mathematics Mathematics - Optimization and Control Mathematics |
| Zdroj: | SIAM Journal on Scientific Computing. 42:A3006-A3029 |
| ISSN: | 1095-7197 1064-8275 |
| DOI: | 10.1137/19m130128x |
| Popis: | Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also non-negative. We propose a formalism and algorithms for preserving certain types of such structure in function approximation. In particular, we consider structure corresponding to a convex constraint on the approximant (for which positivity is one example). The approximation problem then converts into a convex feasibility problem, but the feasible set is relatively complicated so that standard convex feasibility algorithms cannot be directly applied. We propose and discuss different algorithms for solving this problem. One of the features of our machinery is flexibility: relatively complicated constraints, such as simultaneously enforcing positivity, monotonicity, and convexity, are fairly straightforward to implement. We demonstrate the success of our algorithm on several problems in univariate function approximation. |
| Databáze: | OpenAIRE |
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