论文标题
计算Lyapunov操作员φ-函数，并应用于矩阵值指数积分器
Computing the Lyapunov operator φ-functions, with an application to matrix-valued exponential integrators
论文作者
论文摘要
在本文中，我们为Lyapunov操作员函数$φ_l（\ Mathcal {l} _a）[q]，$ $φ_l（\ cdot）$进行有效，准确的评估是与指数相关的函数，$ \ \ \ \ m nathcal {l} _a _a $ is lyapunov is somptrix and $ q是一个symsmentix and-issmentix。该算法的一个重要应用是用于矩阵值的指数积分器，用于矩阵微分方程，例如差异lyapunov方程和差分riccati方程。通过使用修改的缩放和平方步骤与截断的泰勒系列相结合来利用该方法。提出了准回误误分析，以确定缩放参数的值和泰勒近似程度。数值实验表明，该算法在准确性和效率方面表现良好。
In this paper, we develop efficient and accurate evaluation for the Lyapunov operator function $φ_l(\mathcal{L}_A)[Q],$ where $φ_l(\cdot)$ is the function related to the exponential, $\mathcal{L}_A$ is a Lyapunov operator and $Q$ is a symmetric and full-rank matrix. An important application of the algorithm is to the matrix-valued exponential integrators for matrix differential equations such as differential Lyapunov equations and differential Riccati equations. The method is exploited by using the modified scaling and squaring procedure combined with the truncated Taylor series. A quasi-backward error analysis is presented to determine the value of the scaling parameter and the degree of the Taylor approximation. Numerical experiments show that the algorithm performs well in both accuracy and efficiency.
