The aim of this paper is to present construction of finite element multiscaling function with three coefficients. In order to illuminate the result, two examples are given finally.
An algorithm is presented for raising an approximation order of any given orthogonal multiscaling function with the dilation factor a.Letφ(x)=[φ1(x),φ2(x),…,φr(x)]T be an orthogonal multiscaling function with the...An algorithm is presented for raising an approximation order of any given orthogonal multiscaling function with the dilation factor a.Letφ(x)=[φ1(x),φ2(x),…,φr(x)]T be an orthogonal multiscaling function with the dilation factor a and the approximation order m.We can construct a new orthogonal multiscaling functionφnew(x)=[φT(x).f3r+1(x),φr+2(x),…,φr+s(x)}T with the approximation order m+L(L∈Z+).In other words,we raise the approximation order of multiscaling functionφ(x)by increasing its multiplicity.In addition,we discuss an especial setting.That is,if given an orthogonal multiscaling functionφ(x)=[φ1(x),φ2(x),…,φr(x)]T is symmetric,then the new orthogonal multiscaling functionφnew(x)not only raise the approximation order but also preserve symmetry.Finally,some examples are given.展开更多
基金Supported by the Natural Science Foundation of the Education Department of Henan Province(2006110001)Supported by the Natural Science Foundation of Henan University of China (XK03YBSX002)
文摘The aim of this paper is to present construction of finite element multiscaling function with three coefficients. In order to illuminate the result, two examples are given finally.
基金supported by the National Natural Science Foundation of China(Grant No.90104004&10471002)973 project of China(Grant No.G1999075105)+1 种基金the Natural Science Foundation of Guangdong Province(Grant No.05008289&032038)the Doctoral Foundation of Guangdong Province(Grant No.04300917).
文摘An algorithm is presented for raising an approximation order of any given orthogonal multiscaling function with the dilation factor a.Letφ(x)=[φ1(x),φ2(x),…,φr(x)]T be an orthogonal multiscaling function with the dilation factor a and the approximation order m.We can construct a new orthogonal multiscaling functionφnew(x)=[φT(x).f3r+1(x),φr+2(x),…,φr+s(x)}T with the approximation order m+L(L∈Z+).In other words,we raise the approximation order of multiscaling functionφ(x)by increasing its multiplicity.In addition,we discuss an especial setting.That is,if given an orthogonal multiscaling functionφ(x)=[φ1(x),φ2(x),…,φr(x)]T is symmetric,then the new orthogonal multiscaling functionφnew(x)not only raise the approximation order but also preserve symmetry.Finally,some examples are given.
