On Efficient Algorithms for Computing Near-Best Polynomial Approximations to High-Dimensional, Hilbert-Valued Functions From Limited Samples
Sparse polynomial approximation is an important tool for approximating high-dimensional functions from limited samples – a task commonly arising in computational science and engineering. Yet, it lacks a complete theory. There is a well-developed theory of best s-term polynomial approximation, which...
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European Mathematical Society Publishing House
2024
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=nlebk&AN=3900140&site=ehost-live header: @attributes: shortDbName: nlebk uiTerm: 3900140 longDbName: eBook Collection (EBSCOhost) uiTag: AN controlInfo: bkinfo: btl: On Efficient Algorithms for Computing Near-Best Polynomial Approximations to High-Dimensional, Hilbert-Valued Functions From Limited Samples aug: au: Ben Adcock, Simone Brugiapaglia, Nick Dexter, Sebastian Moraga sertl: Memoirs of the European Mathematical Society isbn: 9783985470709 9783985475704 imageinfo: pubinfo: dt: @attributes: year: 2024 month: 01 day: 01 dtAvail: @attributes: year: 2024 month: 06 day: 28 vid: 00013 pub: European Mathematical Society Publishing House pubContract: European Mathematical Society - EMS - Publishing House GmbH place: Berlin price: 0.01 limitsGroup: maxCheckoutDays: 1500 pda: N printPagesOffline: 100 printPagesOnline: 100 previewPages: 10000 prePubGroup: dewey: @attributes: class: 511.4 item: 511 .4 lc: @attributes: class: QA221 .A33 2024eb item: QA 221 .A33 2024eb artinfo: ui: 3900140 1437357730 formats: fmt: @attributes: type: EB doid: NL$3900140$PDF caption: PDF download: Y tig: atl: On Efficient Algorithms for Computing Near-Best Polynomial Approximations to High-Dimensional, Hilbert-Valued Functions From Limited Samples ptl: On Efficient Algorithms for Computing Near-Best Polynomial Approximations to High-Dimensional, Hilbert-Valued Functions From Limited Samples aug: au: Ben Adcock, Simone Brugiapaglia, Nick Dexter, Sebastian Moraga su: Characteristic functions Approximation theory Polynomials sug: subj: SCIENCE / Physics / Mathematical & Computational Characteristic functions Approximation theory Polynomials ab: Sparse polynomial approximation is an important tool for approximating high-dimensional functions from limited samples – a task commonly arising in computational science and engineering. Yet, it lacks a complete theory. There is a well-developed theory of best s-term polynomial approximation, which asserts exponential or algebraic rates of convergence for holomorphic functions. There are also increasingly mature methods such as (weighted) ℓ1-minimization for practically computing such approximations. However, whether these methods achieve the rates of the best s-term approximation is not fully understood. Moreover, these methods are not algorithms per se, since they involve exact minimizers of nonlinear optimization problems. This paper closes these gaps by affirmatively answering the following question: are there robust, efficient algorithms for computing sparse polynomial approximations to finite- or infinite-dimensional, holomorphic and Hilbert-valued functions from limited samples that achieve the same rates as the best s-term approximation? We do so by introducing algorithms with exponential or algebraic convergence rates that are also robust to sampling, algorithmic and physical discretization errors. Our results involve several developments of existing techniques, including a new restarted primal-dual iteration for solving weighted ℓ1-minimization problems in Hilbert spaces. Our theory is supplemented by numerical experiments demonstrating the efficacy of these algorithms. pubtype: eBook doctype: Book ougenre: Book language: English copyright: @attributes: flag: N copyrightText: holdings: @attributes: islocal: N |
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