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For large-scale data fitting, the least-squares progressive iterativeapproximation is a widely used method in many applied domains because of itsintuitive geometric meaning and efficiency. In this work, we present arandomized progressive iterative approximation (RPIA) for the B-spline curveand surface fittings. In each iteration, RPIA locally adjusts the controlpoints according to a random criterion of index selections. The difference foreach control point is computed concerning the randomized block coordinatedescent method. From geometric and algebraic aspects, the illustrations of RPIAare provided. We prove that RPIA constructs a series of fitting curves (resp.,surfaces), whose limit curve (resp., surface) can converge in expectation tothe least-squares fitting result of the given data points. Numericalexperiments are given to confirm our results and show the benefits of RPIA.

Randomized progressive iterative approximation for B-spline curve and surface fittings