Multivariate polynomial interpolation is a method that searches for a polynomial surface that passes through given data points. It is one of the fundamental methods in approximation theory and numerical analysis. Trough interpolation of data points, various 3D shapes can be represented in mathematical form that can be understood by a computer. Because of its simplicity and fine properties, polynomial surfaces are frequently selected from a tensor product surfaces. The interpolation problem is translated into solving a system of linear equations which can be done using various methods. The present study focuses on the solving of linear systems that derives from a bilinear interpolation with tensor product surfaces. This is done by means of Richardson iteration, a numerical iterative method used for solving linear systems. The study discusses three approaches of implementing the method and compares their computational cost based on the properties of the chosen tensor product surface. The paper showcases the process of interpolation of data points on a given function using a Bézier tensor product surface. The system of linear functions is solved taking the three aforementioned approaches and the results are compared.
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