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

Fukang Yin, Jianping Wu, Junqiang Song and Jinhui Yang
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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

Mathematics, 2019, vol. 7, issue 10, 1-15

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.

Keywords: Legendre transform; block partitioning; interpolative decomposition; butterfly algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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