Variation diminishing spline 関数の knots の配置とその多重度の決定について

概要

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In the problem of approximation by spline functions, the decision of knots has a very important influence to approximation accuracy and so on. H.B.Curry & I.J.Schoenberg (1) showed that a spline function S(x) of order m (or degree m-1) with the mutiplicity r of knots belongs to C^<m-1-r> near at their knots. In this paper, we identify the behavior of normalized B-splines and the Properties of variation diminishing spline functions with multiple knots, and present the algorithms to decide the locations and multiplicities of knots. In these algorithms, the rate of convergence in error estimate is improved. Moreover error estimate has an advantage that is related to only the modulus of continuity of function which is approximated by variation diminishing spline functions.
1978-03-15