Verified computed Peano constants and applications in numerical quadrature

Content Provider	Semantic Scholar
Author	Chen, Chin-Yun
Copyright Year	2007
Abstract	Peano kernels are critical for the error estimates of numerical approximation of linear functionals. In the literature, considerable efforts have been devoted to the numerical computation or estimation of Peano constants, however, their discussions have mainly focused on the Peano kernels of some specific higher orders related to the degrees of the underlying error functionals. Limiting to such higher orders either requires certain smoothness of the approximated functions, which is not always fulfilled, or is not always the optimal choice for error estimates, even if the approximated functions are sufficiently smooth. Practical considerations in computing Peano constants for the full range of orders are given in this paper. Numerical examples are also given to demonstrate that much better error bounds can be derived while Peano constants of lower orders are considered.
Starting Page	297
Ending Page	312
Page Count	16
File Format	PDF HTM / HTML
DOI	10.1007/s10543-007-0128-x
Alternate Webpage(s)	https://page-one.springer.com/pdf/preview/10.1007/s10543-007-0128-x
Alternate Webpage(s)	https://doi.org/10.1007/s10543-007-0128-x
Volume Number	47
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article