On Efficient Algorithms for Computing Near-Best Polynomial Approximations to High-Dimensional, Hilbert-Valued Functions from Limited Samples
Ben Adcock
Simon Fraser University, Burnaby, CanadaSimone Brugiapaglia
Concordia University, Montreal, CanadaNick Dexter
Simon Fraser University, Burnaby, CanadaSebastian Moraga
Simon Fraser University, Burnaby, Canada
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This book is published open access.
FrontmatterDownload pp. i–iv | |
AbstractDownload p. v | |
ContentsDownload pp. vii–viii | |
1 | IntroductionDownload pp. 1–9 |
2 | PreliminariesDownload pp. 11–18 |
3 | Problem statement and main resultsDownload pp. 19–30 |
4 | Construction of the algorithmsDownload pp. 31–45 |
5 | Numerical experimentsDownload pp. 47–58 |
6 | Overview of the proofsDownload p. 59 |
7 | Hilbert-valued compressed sensingDownload pp. 61–65 |
8 | Error bounds for polynomial approximation via the Hilbert-valued, weighted SR-LASSODownload pp. 67–73 |
9 | Error bounds and the restarting scheme for the primal-dual iterationDownload pp. 75–79 |
10 | Final argumentsDownload pp. 81–88 |
11 | ConclusionsDownload pp. 89–90 |
A | Best polynomial approximation rates for holomorphic functionsDownload pp. 91–93 |
ReferencesDownload pp. 95–104 |