In this thesis, we focus on methods for interpolation and approximation of functions by splines. We analyze splines in one variable, presenting them in the B-spline basis. We examine their fundamental properties and various interpolation methods such as linear interpolation, Hermite interpolation and not-a-knot interpolation. We also explore quasi-interpolation, shape-preserving spline techniques, and leastsquares approximation. Subsequently, we focus on splines in two variables, where we study splines defined by tensor products and their application in interpolation and approximation. We demonstrate that methods applied to splines in one variable can be extended to splines in two variables. This work contributes to a better understanding of interpolation and approximation techniques, which are essential for various applications in numerical and computational sciences.
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