Range and Domain Partitioning in Piecewise Polynomial Approximation

J. S. C. Prentice

Abstract


Abstract: Error control in piecewise polynomial interpolation of a smooth univariate function f requires that the interval of approximation be subdivided into many subintervals, on each of which an interpolating polynomial is determined. The number of such subintervals is often over- estimated through the use of a high-order derivative of f . We report on a partitioning algorithm, in which we attempt to reduce the number of subintervals required, by imposing conditions on f and its relevant higher derivative. One of these conditions facilitates a distinction between the need for absolute or relative error control. Two examples demonstrate the effectiveness of this partitioning algorithm.
Key Words: Piecewise Polynomial; Range Partitioning; Domain Partitioning; Error Control

Keywords


Piecewise Polynomial; Range Partitioning; Domain Partitioning; Error Control

Full Text:

PDF


DOI: http://dx.doi.org/10.3968/j.sms.1923845220120202.006

DOI (PDF): http://dx.doi.org/10.3968/g1584

Refbacks

  • There are currently no refbacks.


Copyright (c)




Share us to:   


Please send your manuscripts to sms@cscanada.net,or  sms@cscanada.org  for consideration. We look forward to receiving your work.

 

 Articles published in Studies in Mathematical Sciences are licensed under Creative Commons Attribution 4.0 (CC-BY).

 STUDIES IN MATHEMATICAL SCIENCES Editorial Office

Address: 1055 Rue Lucien-L'Allier, Unit #772, Montreal, QC H3G 3C4, Canada.

Telephone: 1-514-558 6138

Http://www.cscanada.net
Http://www.cscanada.org
E-mail:caooc@hotmail.com

Copyright © 2010 Canadian Research & Development Centre of Sciences and Cultures