On Best Approximation by Ridge Functions

AbstractWe consider best approximation of some function classes by the manifold Mn consisting of sums of n arbitrary ridge functions. It is proved that the deviation of the Sobolev class Wr, d2 from the manifold Mn in the space L2 behaves asymptotically as n−r/(d−1)

Approximation of Sobolev classes by polynomials and ridge functions

AbstractLet Wpr(Bd) be the usual Sobolev class of functions on the unit ball Bd in Rd, and Wp∘,r(Bd) be the subclass of all radial functions in Wpr(Bd). We show that for the classes Wp∘,r(Bd) and Wpr(Bd), the orders of best approximation by polynomials in Lq(Bd) coincide. We also obtain exact orders of best approximation in L2(Bd) of the classes Wp∘,r(Bd) by ridge functions and, as an immediate consequence, we obtain the same orders in L2(Bd) for the usual Sobolev classes Wpr(Bd)

Calculations of parameters of laser quenching with scanning

22.00; Translated from Russian (Fiz. Khim. Obrab. Mater. 1989 v. 23(1) p. 38-43)Available from British Library Document Supply Centre- DSC:9023.19(VR-Trans--4389)T / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo