Order of the best spline approximations of some classes of functions |
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Authors: | Yu N Subbotin N I Chernykh |
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Institution: | (1) V. A. Steklov Mathematics Institute, Sverdlovsk Branch, Academy of Science of the USSR, USSR |
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Abstract: | The rate of decrease of the upper bounds of the best spline approximations Em,n(f)p with undetermined n nodes in the metric of the space Lp(0, 1) (1p) is studied in a class of functionsf(x) for which f
m+1 (x)Lq(0, 1)1(1qt8) or var {f(m) (x); 0, 1}1 (m=1, 2, ..., the preceding derivative is assumed absolutely continuous). An exact order of decrease of the mentioned bounds is found as n , and asymptotic formulas are obtained for p= and 1q in the case of an approximation by broken lines (m=1). The simultaneous approximation of the function and its derivatives by spline functions and their appropriate derivatives is also studied.Translated from Matematicheskie Zametki, Vol. 7, No. 1, pp. 31–42, January, 1970. |
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