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… Click to show full 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(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.
Journal Title: Mathematics
Year Published: 2019
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