Treffer: One method for searching the best discrete TL_p approximation: One method for searching the best discrete \(TL_p\) approximation

Title:
One method for searching the best discrete TL_p approximation: One method for searching the best discrete \(TL_p\) approximation
Authors:
Baumgartner, Alfonzo, Sabo, Kristian
Source:
Mathematical communications. Supplement. 1(1):63
Publisher Information:
Croatian Mathematical Society, Division Osijek, Osijek, 2001.
Publication Year:
2001
Subject Terms:
numerical examples, \(L_p\) norm, Spline approximation, Brent method, Nelder-Meads downhill simplex method, curve of second order, discrete TL_p approximation, natural cubic spline, Numerical computation using splines
Document Type:
Fachzeitschrift Article
File Description:
application/xml
Language:
English
ISSN:
1333-0829
Access URL:
https://www.bib.irb.hr/58559
https://zbmath.org/1679596
Accession Number:
edsair.dedup.wf.002..156736dd1875a855876e703aa1bfa165
Database:
OpenAIRE

Weitere Informationen

On the basis of the given data we will show how efficiently the best TL_p natural cubic spline can be found. Cases p=1, 2 will be especially considered. The best TL_1 spline is of special interest because it is insensitive to the so called outliers, although for its constuction it is necessary to carry out a multidimensional minimization of an undifferetiable function. For that purpose Nelder-Meads Downhill Simplex Method is used. For the calculation of the distance from the data-point to the spline the Brent Method for onedimensional minimization is used. Also, based on the described methods we will show generating of the optimal curve of the second order on the basis of the given data. The method is illustrated with examples developed on the basis of our own programs written in the C programming language.