古拉格切蛋糕

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Asymptotic Property of Approximation to x~αsgnx by Newman Type Operators

The approximation of |x| by rational functions is a classical rational problem.This paper deals with the rational approximation of the function x~αsgnx, which equals |x| ifα=1.We construct a Newman type operator r_n(x) and show {|x~αsgnx-r_n(x)|}～Cn~(-(α/2)e-(2nα)~(1/2)), where C is a constant depending onα.     

本刊英文版Vol.28(2012),No.12论文摘要

<正>Nordhaus-Gaddum Results for the Sum of the Induced Path Number of a Graph and Its Complement Johannes H.HATTINGH Lucas C.VAN DER MERWE Ossama A.SALEH Terry J.WALTERS     

MULTIGRID METHODS FOR OBSTACLE PROBLEMS

In this review,we intend to clarify the underlying ideas and the relations between various multigrid methods ranging from subset decomposition,to projected subspace decomposition and truncated multigrid.In addition,we present a novel globally convergent inexact active set method which is closely related to truncated multigrid.The numerical properties of algorithms are carefully assessed by means of a degenerate problem and a problem with a complicated coincidence set.