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On Efficient Algorithms for Computing Near-Best Polynomial Approximations to High-Dimensional, Hilbert-Valued Functions from Limited Samples

  • Ben Adcock

    Simon Fraser University, Burnaby, Canada

  • Simone Brugiapaglia

    Concordia University, Montreal, Canada

  • Nick Dexter

    Simon Fraser University, Burnaby, Canada

  • Sebastian Moraga

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