2009
DOI: 10.1093/imanum/drp008
|View full text |Cite
|
Sign up to set email alerts
|

Piecewise-smooth chebfuns

Abstract: Abstract. Algorithms are described that make it possible to manipulate piecewise-smooth functions on real intervals numerically with close to machine precision. Breakpoints are introduced in some such calculations at points determined by numerical rootfinding, and in others by recursive subdivision or automatic edge detection. Functions are represented on each smooth subinterval by Chebyshev series or interpolants. The algorithms are implemented in object-oriented Matlab in an extension of the chebfun system, … Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
2

Citation Types

0
61
0

Year Published

2010
2010
2021
2021

Publication Types

Select...
6
1

Relationship

1
6

Authors

Journals

citations
Cited by 44 publications
(61 citation statements)
references
References 14 publications
0
61
0
Order By: Relevance
“…The chebfun system also handles piecewise smooth functions [12]. Piecewise representations can result from certain operations on smooth functions such as abs, sign, floor, ceil, round, fix, min, max among others.…”
Section: Piecewise Representationsmentioning
confidence: 99%
See 2 more Smart Citations
“…The chebfun system also handles piecewise smooth functions [12]. Piecewise representations can result from certain operations on smooth functions such as abs, sign, floor, ceil, round, fix, min, max among others.…”
Section: Piecewise Representationsmentioning
confidence: 99%
“…The breakpoints are stored in the field f.ends. The edge detection algorithm uses bisection and finite differences to locate jumps in function values accurately to machine precision, as well as jumps in first, second and third derivatives [12]. In splitting off mode, the system disables the splitting algorithm.…”
Section: Piecewise Representationsmentioning
confidence: 99%
See 1 more Smart Citation
“…A third technique is the automatic subdivision of an interval in "splitting on" mode, allowing representation of very general singularities at some cost in speed and smoothness. Detailed in [16], this strategy is similar to the hpadaptivity commonly employed in finite element methods.…”
Section: Introductionmentioning
confidence: 99%
“…Chebyshev thinking reached an apotheosis of sorts in the MATLAB extension Chebfun developed recently by Trefethen and collaborators [53,2,47,32]. MATLAB was originally created by Cleve Moler as a system for manipulating vector and matrices, morphing over the years into a full-featured programming language and visualization system.…”
mentioning
confidence: 99%