Fast Analytic Sampling Approximation from Cauchy Kernel. (15th March 2016) - Li, Youfa; Shang, Jing; Yang, Honglei; Zhang, Gengrong; Yang, Shouzhi
Abstract : The paper aims at establishing a fast numerical algorithm for B k ( f ), where f is any function in the Hardy space H 2 ( T d ) and k is the scale level. Here, B k ( f ) is an approximation to f we recently constructed by applying the multiscale transform to the Cauchy kernel. We establish the matrix expression of B k ( f ) and find that it has the structure of a multilevel Hankel matrix. Based on the structure, a fast numerical algorithm is established to compute B k ( f ) . The computational complexity is given. A numerical experiment is carried out to check the efficiency of our algorithm.