An SVD analysis of equispaced polynomial interpolation

Runge showed more than a century ago that polynomial interpolation of degree N on a uniform, evenly-spaced grid may diverge as N → ∞ . Here, we present a new angle on polynomial interpolation and the Runge Phenomenon by performing an SVD analysis of the interpolation matrix. We prove that the observ...

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Bibliographic Details
Published in:	Applied numerical mathematics Vol. 59; no. 10; pp. 2534 - 2547
Main Authors:	Boyd, John P., Sousa, Alan M.
Format:	Journal Article
Language:	English
Published:	Kidlington Elsevier B.V 01.10.2009 Elsevier
Subjects:	Approximations and expansions Exact sciences and technology Interpolation Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical approximation Polynomial interpolation Runge Phenomenon Sciences and techniques of general use SVD analysis Interpolation Runge Phenomenon Polynomial interpolation SVD analysis Polynomial Matrix analysis Filtering Grid pattern Error estimation Singular value Numerical approximation Numerical analysis Applied mathematics Condition number Growth of error
ISSN:	0168-9274, 1873-5460
Online Access:	Get full text
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