A symmetry and bi-recursive algorithm of accurately computing Krawtchouk moments

  • Authors:

  • Guojun Zhang;Zhu Luo;Bo Fu;Bo Li;Jiaping Liao;Xiuxiang Fan;Zheng Xi

  • Affiliations:

  • School of Mechanical Science and Engineering, Huazhong University of Science and Technology, 430074 Wuhan, China;School of Electrical and Electronic Engineering, Hubei University of Technology, 430068 Wuhan, China;School of Electrical and Electronic Engineering, Hubei University of Technology, 430068 Wuhan, China;School of Mechanical Science and Engineering, Huazhong University of Science and Technology, 430074 Wuhan, China;School of Electrical and Electronic Engineering, Hubei University of Technology, 430068 Wuhan, China;School of Electrical and Electronic Engineering, Hubei University of Technology, 430068 Wuhan, China;School of Electrical and Electronic Engineering, Hubei University of Technology, 430068 Wuhan, China

  • Venue:
  • Pattern Recognition Letters
  • Year:
  • 2010

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Abstract

Few scientific studies have discussed the accuracy of the Krawtchouk moments for the common case of p0.5. In the paper, a novel symmetry and bi-recursive algorithm is proposed to accurately calculate the Krawtchouk moments for the case of p@? (0, 1). The numerical propagation error mechanism of direct recursively calculating the Krawtchouk moments is first analyzed. It reveals that the recursion coefficients and recurrence times of the three-term recurrence relations are the key factors of reducing the propagation error in the computation of the Krawtchouk moment of high order. Based on the analysis, the x-n plane is divided into four parts by x=n and x+n=N-1. We use the n-ascending recurrence formula to calculate the polynomials in the domain of N-1-n=x=n=0 and apply the n-descending recurrence relations in the domain of 0=