On Bivariate Haar Functions and Interpolation Polynomial

Volume 10, Issue 2, pp 100-112 http://dx.doi.org/10.22436/jmcs.010.02.03

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Authors

R. Dehghan - Department of Mathematics, Islamic Azad University, Masjed Soleiman branch, Masjed Soleiman, Iran. K. Rahsepar Fard - Department of Computer Engineering, University of Qom, Qom, Iran.

Abstract

In this paper we consider bivariate Haar series in general case, where bivariate Haar functions are defined on the plane. Here we define a new bivariate Haar function that is included two independent variables. Indeed we presented the new function that is not in previous researches. Mathematicians have applied bivariate Haar function based on tensor product that is a special case of bivariate case. In this research we define the Haar functions by applying another way. Therefore, we define the Haar function differently. And also, the interpolation polynomial with two variables is explained. Then we compare two methods for calculating the approximating function. Namely, we consider a numerical example for comparing the new approximation to bivariate interpolation polynomial. In this example we compute interpolation polynomial by points with Newton lattice form. The calculations indicate that the accuracy of the obtained solutions is acceptable when the number of calculation points is small.

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Keywords

• Bivariate Haar function
• Bivariate interpolation polynomial
• Haar Fourier coefficient
• Haar series

MSC

•  65D05
•  42C10

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