In this thesis, we focus on quasi-interpolation. In classical interpolation, the goal is to draw a curve through all given points, which often results in a large system of linear equations. Quasi-interpolation, on the other hand, involves solving several smaller, local systems. With quasi-interpolation, we do not interpolate the points directly; instead, we approximate them sufficiently well. Our approach begins by examining an example of interpolation with polynomials, followed by the definition and explanation of the fundamental building blocks of quasi-interpolants, namely B-splines. We then formally define quasi-interpolation and prove the order of convergence for chosen quasi-interpolants. Throughout the thesis, we implement the derived methods and present them graphically. Finally, we derive the local method of least squares and explore a practical application of quasi-interpolation in noise removal from a signal.
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