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Fast Hankel Transforms Algorithm Based on Kernel Function Interpolation with Exponential Functions

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Listed:
  • Huaiqing Zhang
  • Yu Chen
  • Xin Nie

Abstract

The Pravin method for Hankel transforms is based on the decomposition of kernel function with exponential function. The defect of such method is the difficulty in its parameters determination and lack of adaptability to kernel function especially using monotonically decreasing functions to approximate the convex ones. This thesis proposed an improved scheme by adding new base function in interpolation procedure. The improved method maintains the merit of Pravin method which can convert the Hankel integral to algebraic calculation. The simulation results reveal that the improved method has high precision, high efficiency, and good adaptability to kernel function. It can be applied to zero‐order and first‐order Hankel transforms.

Suggested Citation

  • Huaiqing Zhang & Yu Chen & Xin Nie, 2014. "Fast Hankel Transforms Algorithm Based on Kernel Function Interpolation with Exponential Functions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:105469
    DOI: 10.1155/2014/105469
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    References listed on IDEAS

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    1. E. B. Postnikov, 2003. "About calculation of the Hankel transform using preliminary wavelet transform," Journal of Applied Mathematics, Hindawi, vol. 2003, pages 1-7, January.
    2. E. B. Postnikov, 2003. "About calculation of the Hankel transform using preliminary wavelet transform," Journal of Applied Mathematics, John Wiley & Sons, vol. 2003(6), pages 319-325.
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