About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

Révayová, Martina ; Török, Csaba
Reference points based recursive approximation. (English). Kybernetika, vol. 49 (2013), issue 1, pp. 60-72
MSC: 41A10, 62-07, 62F10, 62J05, 62L12, 65D05, 65D07, 65D10
Keywords:
approximation model; consistency; asymptotic normality
Summary:
The paper studies polynomial approximation models with a new type of constraints that enable to get estimates with significant properties. Recently we enhanced a representation of polynomials based on three reference points. Here we propose a two-part cubic smoothing scheme that leverages this representation. The presence of these points in the model has several consequences. The most important one is the fact that by appropriate location of the reference points the resulting approximant of two successively assessed neighboring approximants will be smooth. We also show that the considered models provide estimates with appropriate statistical properties such as consistency and asymptotic normality.
References:
[1] Dikoussar, N. D.: Adaptive projective filters for track finding. Comput. Phys. Commun. 79 (1994), 39-51. DOI 10.1016/0010-4655(94)90228-3
[2] Dikoussar, N. D.: Kusochno-kubicheskoje priblizhenije I sglazhivanije krivich v rezhime adaptacii. Comm. JINR, P10-99-168, Dubna 1999.
[3] Dikoussar, N. D., Török, Cs.: Automatic knot finding for piecewise-cubic approximation. Mat. Model. T-17 (2006), 3. MR 2255951 | Zbl 1099.65014
[4] Dikoussar, N. D., Török, Cs.: Approximation with DPT. Comput. Math. Appl. 38 (1999), 211-220. MR 1718884
[5] Haykin, S.: Adaptive Filter Theory. Prentice Hall, 2002 Zbl 0723.93070
[6] Nadaraya, E. A.: On estimating regression. Theory Probab. Appl. 9 (1964 ), 141-142. Zbl 0136.40902
[7] Reinsch, Ch. H.: Smoothing by spline functions. Numer. Math. 10 (1967), 177-183. DOI 10.1007/BF02162161 | MR 0295532 | Zbl 1248.65020
[8] Révayová, M., Török, Cs.: Piecewise approximation and neural networks. Kybernetika 43 (2007), 4, 547-559. MR 2377932 | Zbl 1145.68495
[9] Ripley, B. D.: Pattern Recognision and Neural Networks. Cambridge University Press, 1996. MR 1438788
[10] Török, Cs.: 4-point transforms and approximation. Comput. Phys. Commun. 125 (2000), 154-166. DOI 10.1016/S0010-4655(99)00483-X | Zbl 0976.65011
[11] Wasan, M. T.: Stochastic Approximation. Cambridge University Press, 2004. MR 0247712 | Zbl 0271.62112
Partner of
EuDML logo