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Title: On the Lebesgue constant of weighted Leja points for Lagrange interpolation on unbounded domains

Abstract

Here, this work focuses on weighted Lagrange interpolation on an unbounded domain and analyzes the Lebesgue constant for a sequence of weighted Leja points. The standard Leja points are a nested sequence of points defined on a compact subset of the real line and can be extended to unbounded domains with the introduction of a weight function w:R → [0,1]⁠. Due to a simple recursive formulation in one dimension, such abscissas provide a foundation for high-dimensional approximation methods such as sparse grid collocation, deterministic least squares and compressed sensing. Just as in the unweighted case of interpolation on a compact domain, we use results from potential theory to prove that the Lebesgue constant for the Leja points grows subexponentially with the number of interpolation nodes.

Authors:
 [1]; ORCiD logo [2]; ORCiD logo [3]
  1. Univ. of Tennessee, Knoxville, TN (United States)
  2. Univ. of Tennessee, Knoxville, TN (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1559607
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
IMA Journal of Numerical Analysis
Additional Journal Information:
Journal Volume: 39; Journal Issue: 2; Journal ID: ISSN 0272-4979
Publisher:
Oxford University Press/Institute of Mathematics and its Applications
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; weighted Leja sequence; Lagrange interpolation; Lebesgue constant

Citation Formats

Jantsch, Peter, Webster, Clayton G., and Zhang, Guannan. On the Lebesgue constant of weighted Leja points for Lagrange interpolation on unbounded domains. United States: N. p., 2018. Web. doi:10.1093/imanum/dry002.
Jantsch, Peter, Webster, Clayton G., & Zhang, Guannan. On the Lebesgue constant of weighted Leja points for Lagrange interpolation on unbounded domains. United States. doi:10.1093/imanum/dry002.
Jantsch, Peter, Webster, Clayton G., and Zhang, Guannan. Sat . "On the Lebesgue constant of weighted Leja points for Lagrange interpolation on unbounded domains". United States. doi:10.1093/imanum/dry002. https://www.osti.gov/servlets/purl/1559607.
@article{osti_1559607,
title = {On the Lebesgue constant of weighted Leja points for Lagrange interpolation on unbounded domains},
author = {Jantsch, Peter and Webster, Clayton G. and Zhang, Guannan},
abstractNote = {Here, this work focuses on weighted Lagrange interpolation on an unbounded domain and analyzes the Lebesgue constant for a sequence of weighted Leja points. The standard Leja points are a nested sequence of points defined on a compact subset of the real line and can be extended to unbounded domains with the introduction of a weight function w:R → [0,1]⁠. Due to a simple recursive formulation in one dimension, such abscissas provide a foundation for high-dimensional approximation methods such as sparse grid collocation, deterministic least squares and compressed sensing. Just as in the unweighted case of interpolation on a compact domain, we use results from potential theory to prove that the Lebesgue constant for the Leja points grows subexponentially with the number of interpolation nodes.},
doi = {10.1093/imanum/dry002},
journal = {IMA Journal of Numerical Analysis},
number = 2,
volume = 39,
place = {United States},
year = {2018},
month = {6}
}

Journal Article:
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