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.

翻译：本文提出了一种高效计算一般振荡矩阵函数的算法。此类计算对于求解二阶半线性初值问题至关重要。该方法基于四倍角公式的缩放与恢复技术，结合截断泰勒级数实现。缩放参数的选择与泰勒多项式次数的确定依赖于前向误差分析。数值实验表明，新算法运行稳定，在精度与效率方面均表现优异。