Positive and Copositive Spline Approximation in L P 0; 1]
نویسنده
چکیده
The order of positive and copositive spline approximation in the L p-norm, 1 p < 1, is studied, the main results are (1) the error of positive approximation by splines is bounded by C! 2 (f; 1=n) p if f has a nonnegative extension; (2) the order deteriorates to ! 1 if f does not have such an extension; (3) the error of copositive spline approximation is bounded by C!(f; 1=n) p ; (4) if f is also continuous, the error in (3) can be estimated in terms of the third-modulus 3 (f; 1=n) p. All constants in the error bounds are absolute.
منابع مشابه
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تاریخ انتشار 1995