id: 01679596
dt: j
an: 01679596
au: Sabo, Kristian; Baumgartner, Alfonzo
ti: One method for searching the best discrete $TL_p$ approximation.
so: Math. Commun., Suppl. 1, No.1, 63-68 (2001).
py: 2001
pu: Croatian Mathematical Society, Division Osijek, Osijek
la: EN
cc: 
ut: numerical examples; natural cubic spline; $L_p$ norm; curve of second
    order; Nelder-Meads downhill simplex method; Brent method
ci: 
li: 
ab: Summary: On the basis of the given data we show how efficiently the best
    $TL_p$ natural cubic spline can be found. The 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
    construction it is necessary to carry out a multidimensional
    minimization of an undifferentiable function. For that purpose the
    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 show the generating of the optimal curve of second order on
    the basis of the given data. The method is illustrated by examples
    developed on the basis of our own programs written in the C programming
    language.
rv: