Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

IMPACT FACTOR 2018: 1.218
5-year IMPACT FACTOR: 1.411

CiteScore 2018: 1.42

SCImago Journal Rank (SJR) 2018: 0.947
Source Normalized Impact per Paper (SNIP) 2018: 0.939

Mathematical Citation Quotient (MCQ) 2018: 1.22

See all formats and pricing
More options …
Volume 12, Issue 4


Polynomial of Best Uniform Approximation to 1/x and Smoothing in Two-level Methods

Johannes Kraus
  • Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences Altenberger Str. 69, 4040 Linz, Austria.
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Panayot Vassilevski
  • Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, P.O. Box 808, L-560, Livermore, CA 94551, U.S.A.
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Ludmil Zikatanov


We derive defect correction scheme for constructing the sequence of polynomials of best approximation in the uniform norm to 1/x on a finite interval with positive endpoints. As an application, we consider two-level methods for scalar elliptic partial differential equation (PDE), where the relaxation on the fine grid uses the aforementioned polynomial of best approximation. Based on a new smoothing property of this polynomial smoother that we prove, combined with a proper choice of the coarse space, we obtain as a corollary, that the convergence rate of the resulting two-level method is uniform with respect to the mesh parameters, coarsening ratio and PDE coefficient variation.

Keywords: polynomial smoothing; best uniform approximation; two-level methods; elliptic problems with large coefficient variation

About the article

Received: 2012-05-08

Revised: 2012-08-28

Accepted: 2012-08-29

Published in Print:

Citation Information: Computational Methods in Applied Mathematics Comput. Methods Appl. Math., Volume 12, Issue 4, Pages 448–468, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.2478/cmam-2012-0026.

Export Citation

© Institute of Mathematics, NAS of Belarus.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

S.K. Tomar
Computers & Mathematics with Applications, 2013, Volume 66, Number 6, Page 1024
Xiaozhe Hu, Panayot S. Vassilevski, and Jinchao Xu
Numerical Linear Algebra with Applications, 2016, Volume 23, Number 4, Page 746
Johannes Kraus, Raytcho Lazarov, Maria Lymbery, Svetozar Margenov, and Ludmil Zikatanov
SIAM Journal on Scientific Computing, 2016, Volume 38, Number 2, Page A875
Paola F. Antonietti, Marco Verani, and Ludmil Zikatanov
Computers & Mathematics with Applications, 2015, Volume 70, Number 11, Page 2674
J. Kraus, M. Lymbery, and S. Margenov
Numerical Linear Algebra with Applications, 2015, Volume 22, Number 6, Page 965
K.P.S. Gahalaut, S.K. Tomar, and J.K. Kraus
Computer Methods in Applied Mechanics and Engineering, 2013, Volume 266, Page 40
Ionela Moale and Veronika Pillwein
LMS Journal of Computation and Mathematics, 2014, Volume 17, Number 01, Page 233

Comments (0)

Please log in or register to comment.
Log in