Information Technology Journal1812-56381812-5646Asian Network for Scientific Information10.3923/itj.2011.2196.2201PeixinYe XuehuaLi 1120111011We studied the optimal convergence rate of algorithm for approximation
and integration problems from some periodic analytic classes. For approximation
problem we determine the optimal convergence rate of Dirichlet interpolating
algorithm over periodic functions
admitting analytic regularities. The optimal order of m-th minimum linear intrinsic
error is also determined. By means of previous results about n-widths, we discuss
the optimality of interpolation method. For integration problem we determine
the optimal convergence rate of the rectangle formula over the class .
We conjecture that the rectangle formula is optimal among all linear quadrature
formulas.]]>Novak, E. and H. Wozniakowski2008Smale, S. and D.X. Zhou,2003Traub, J.F., G.W. Wasilkowski and H. Wozniakowski,1988Temlyakov, V.N.,1985Temlyakov, V.N.,1994Kushpel, A.K.,1990q.]]>