Multivariate filter banks with a polyphase matrix built by matrix factorization(latticestructure)were proposed to obtain orthonormal wavelet basis.On the basis of that,we propose ageneral method of constructing filter banks which ensure second and third accuracy of its correspondingscaling function.In the last part,examples with second and third accuracy are given.
In the present paper,we discuss some properties of piecewise linear spec- tral sequences introduced by Liu and Xu.We have a study on the pointwiso and almost everywhere convergence of its corresponding series.Also,it is shown that the set g constructed from piecewise linear spectral sequences are bases,but not uncon- ditional bases,for L^P(0,1)where 1
We propose a fully discrete fast Fourier-Galerkin method for solving an integral equation of the first kind with a logarithmic kernel on a smooth open arc,which is a reformulation of the Dirichlet problem of the Laplace equation in the plane.The optimal convergence order and quasi-linear complexity order of the proposed method are established.A precondition is introduced.Combining this method with an efficient numerical integration algorithm for computing the single-layer potential defined on an open arc,we obtain the solution of the Dirichlet problem on a smooth open arc in the plane.Numerical examples are presented to confirm the theoretical estimates and to demonstrate the efficiency and accuracy of the proposed method.
WANG Bo1,WANG Rui2 & XU YueSheng3,4,1Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China
