Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Boosted optimal weighted least-squares
HTML articles powered by AMS MathViewer

by Cécile Haberstich, Anthony Nouy and Guillaume Perrin HTML | PDF
Math. Comp. 91 (2022), 1281-1315 Request permission


This paper is concerned with the approximation of a function $u$ in a given subspace $V_m$ of dimension $m$ from evaluations of the function at $n$ suitably chosen points. The aim is to construct an approximation of $u$ in $V_m$ which yields an error close to the best approximation error in $V_m$ and using as few evaluations as possible. Classical least-squares regression, which defines a projection in $V_m$ from $n$ random points, usually requires a large $n$ to guarantee a stable approximation and an error close to the best approximation error. This is a major drawback for applications where $u$ is expensive to evaluate. One remedy is to use a weighted least-squares projection using $n$ samples drawn from a properly selected distribution. In this paper, we introduce a boosted weighted least-squares method which allows to ensure almost surely the stability of the weighted least-squares projection with a sample size close to the interpolation regime $n=m$. It consists in sampling according to a measure associated with the optimization of a stability criterion over a collection of independent $n$-samples, and resampling according to this measure until a stability condition is satisfied. A greedy method is then proposed to remove points from the obtained sample. Quasi-optimality properties in expectation are obtained for the weighted least-squares projection, with or without the greedy procedure. The proposed method is validated on numerical examples and compared to state-of-the-art interpolation and weighted least-squares methods.
Similar Articles
Additional Information
  • Cécile Haberstich
  • Affiliation: CEA, DAM, DIF, F-91297 Arpajon, France
  • ORCID: 0000-0003-4088-3912
  • Email:
  • Anthony Nouy
  • Affiliation: Centrale Nantes, LMJL UMR CNRS 6629, France
  • MR Author ID: 702952
  • Email:
  • Guillaume Perrin
  • Affiliation: CEA, DAM, DIF, F-91297 Arpajon, France
  • Address at time of publication: COSYS, Université Gustave Eiffel, 77420 Champs-sur-Marne, France
  • MR Author ID: 1009710
  • ORCID: 0000-0002-0592-6094
  • Email:
  • Received by editor(s): July 4, 2020
  • Received by editor(s) in revised form: June 28, 2021, and October 11, 2021
  • Published electronically: January 5, 2022
  • © Copyright 2022 American Mathematical Society
  • Journal: Math. Comp. 91 (2022), 1281-1315
  • MSC (2020): Primary 41A10, 41A65, 93E24, 65D05, 65D15
  • DOI:
  • MathSciNet review: 4405496