L2 AND L1 CONTROL THEORETIC SMOOTHING SPLINES
Alaeddin Malek1, Mohammad Asadollahi2
1,2Department of Applied Mathematics
Faculty of Mathematical Sciences
Tarbiat Modares University
P.O. Box 14115-134, Tehran, IRAN

Abstract

L1 and L2 control theoretic splines are effective for Gaussian noise in data since estimations are based on L1 and L2 optimization. Here, it is shown that the result is not robust against outliers for L2 control theoretic splines. Numerical simulations for both y(t) and dy/dt under Gaussian and Laplacian noise are given. It is shown that for meaningful sampling data (number of data more than 75) the L1 control theoretic spline has better performance than L2 control theoretic spline. Numerical results and graphs for minimum, maximum and mean errors are given.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 29
Issue: 6
Year: 2016

DOI: 10.12732/ijam.v29i6.3

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