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Optimal smoothing spline curves and contour synthesis

Abstract We consider a problem of designing optimal smoothing spline curves using normalized uniform B-splines as basis functions. Assuming that the data for smoothing is obtained by sampling some curve with noises, an expression for optimal curves is derived when the number of data becomes infinity. It is then shown that, under certain condition, optimal smoothing splines converge to this curve as the number of data increases. The design method and analyses are extended to the case of periodic splines. Results of numerical experiments for periodic case are included for contour synthesizing problem.