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A High Accurate and Stable Legendre Transform Based on Block Partitioning and Butterfly Algorithm for NWP

Author

Listed:
  • Fukang Yin

    (College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China)

  • Jianping Wu

    (College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China)

  • Junqiang Song

    (College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China)

  • Jinhui Yang

    (College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China)

Abstract

In this paper, we proposed a high accurate and stable Legendre transform algorithm, which can reduce the potential instability for a very high order at a very small increase in the computational time. The error analysis of interpolative decomposition for Legendre transform is presented. By employing block partitioning of the Legendre-Vandermonde matrix and butterfly algorithm, a new Legendre transform algorithm with computational complexity O ( N log 2 N /loglog N ) in theory and O( N log 3 N ) in practical application is obtained. Numerical results are provided to demonstrate the efficiency and numerical stability of the new algorithm.

Suggested Citation

  • Fukang Yin & Jianping Wu & Junqiang Song & Jinhui Yang, 2019. "A High Accurate and Stable Legendre Transform Based on Block Partitioning and Butterfly Algorithm for NWP," Mathematics, MDPI, vol. 7(10), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:966-:d:276135
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