The thesis discusses geometric iterative methods for data approximation using curves, with an emphasis on B-splines. After an introductory presentation of Bézier curves and the de Casteljau algorithm, we define B-splines and the progressive iterative approximation (PIA) method, along with its variants such as WPIA, Jacobi–PIA, GS–PIA, and SOR–PIA. The methods are also presented in their matrix form. To improve the convergence rate, we introduce an appropriate preconditioner and analyze its impact on the efficiency of the methods. Both the basic and preconditioned methods are applied to examples and compared.
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