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

College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China
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Mathematics 2019, 7(10), 966; https://doi.org/10.3390/math7100966
Received: 21 September 2019 / Revised: 4 October 2019 / Accepted: 10 October 2019 / Published: 14 October 2019
(This article belongs to the Section Mathematics and Computer Science)
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(Nlog2N /loglogN) in theory and O(Nlog3N) in practical application is obtained. Numerical results are provided to demonstrate the efficiency and numerical stability of the new algorithm. View Full-Text
Keywords: Legendre transform; block partitioning; interpolative decomposition; butterfly algorithm Legendre transform; block partitioning; interpolative decomposition; butterfly algorithm
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Yin, F.; Wu, J.; Song, J.; Yang, J. A High Accurate and Stable Legendre Transform Based on Block Partitioning and Butterfly Algorithm for NWP. Mathematics 2019, 7, 966.

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