A unified approach to the data fitting problem

 ” A unified approach to the data fitting problem” , L.Gevorgyan …  2016  ,  No . 1 , P. 20 – 30   ,   DOI  :  http://dx.doi.org/10.22039/cjcme.2016.02

Abstract :  

From Wikipedia, the free encyclopedia “Curve fitting is the process of constructing a curve,or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a “smooth” function is constructed that approximately fits the data.  Fitted curves can be used as an aid for data visualization, to infer values of a function where no data are available, and to summarize the relationships among two or more variables.”

We analyze some interpolation and approximation methods and propose a general method of data fitting procedure. Two computer programs are presented.

                                                             References :
1.  W. Cheney, W. Light. A course in approximation theory. Reprint of the 2000 original. Graduate Studies in Mathematics, 101. American Mathematical Society, Providence, RI, 2009. xvi+359 pp. ISBN: 978-0-8218-4798-5 MR2474372 (2010d:41001)
2.  P. J. Davis, Interpolation and approximation, Dover, New York, 1975. MR0380189 (52 ,#1089)
3.  P. P Korovkin, Linear operators and approximation theory. Translated from the Russian ed. (1959). Russian Monographs and Texts on Advanced Mathematics and Physics, Vol. III. Gordon and Breach Publishers, Inc., New York; Hindustan Publishing Corp. (India), Delhi 1960 vii+222 pp.
4.  P. Lancaster, K. Salkauskas, Curve and surface fitting, Academic Press, London, 1986. MR1001969 (90g:65018)
5.  C. Runge, Uber empirische Funktionen und die Interpolation zwischen aquidistanten ordinaten, Zeitschrift fur Mathematik und Physik, 46, (1901), pp. 224-243.