Efficient algorithm for the oscillatory matrix functions

2024/06/10 by Dongping Li, Xue Wang, Li, Dongping +3
Computer Science · #65F30 #65F60 #FOS: Mathematics #G.1.3 #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2406.06008

openalex publication_date 2024/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and restoring technique based on a quadruple angle formula in conjunction with a truncated Taylor series. The choice of the scaling parameter and the degree of the Taylor polynomial relies on a forward error analysis. Numerical experiments show that the new algorithm behaves in a stable fashion and performs well in both accuracy and efficiency.

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