Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 
 

 

A local Lagrange interpolation method based on $ C^{1}$ cubic splines on Freudenthal partitions


Authors: Gero Hecklin, Günther Nürnberger, Larry L. Schumaker and Frank Zeilfelder
Journal: Math. Comp. 77 (2008), 1017-1036
MSC (2000): Primary 41A15, 41A05, 65D05, 65D07, 65D17, 41A63
DOI: https://doi.org/10.1090/S0025-5718-07-02056-X
Published electronically: November 20, 2007
MathSciNet review: 2373190
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A trivariate Lagrange interpolation method based on $ C^{1}$ cubic splines is described. The splines are defined over a special refinement of the Freudenthal partition of a cube partition. The interpolating splines are uniquely determined by data values, but no derivatives are needed. The interpolation method is local and stable, provides optimal order approximation, and has linear complexity.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 41A15, 41A05, 65D05, 65D07, 65D17, 41A63

Retrieve articles in all journals with MSC (2000): 41A15, 41A05, 65D05, 65D07, 65D17, 41A63


Additional Information

Gero Hecklin
Affiliation: Institute for Mathematics, University of Mannheim, 68131 Mannheim, Germany
Email: hecklin@web.de

Günther Nürnberger
Affiliation: Institute for Mathematics, University of Mannheim, 68131 Mannheim, Germany
Email: nuern@rumms.uni-mannheim.de

Larry L. Schumaker
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
Email: larry.schumaker@vanderbilt.edu

Frank Zeilfelder
Affiliation: Institute for Mathematics, University of Mannheim, 68131 Mannheim, Germany
Email: zeilfeld@math.uni-mannheim.de

DOI: https://doi.org/10.1090/S0025-5718-07-02056-X
Keywords: Trivariate splines, local Lagrange interpolation, Freudenthal partitions
Received by editor(s): August 17, 2006
Received by editor(s) in revised form: February 16, 2007
Published electronically: November 20, 2007
Article copyright: © Copyright 2007 American Mathematical Society

American Mathematical Society