论文标题
一种用于求解lyapunov操作员$φ$ functions的低级算法
A low-rank algorithm for solving Lyapunov operator $φ$-functions within the matrix-valued exponential integrators
论文作者
论文摘要
在这项工作中，我们提出了一种低级算法，用于计算大型Lyapunov操作员$φ$函数的低级别近似值。这些计算在实施大规模硬矩阵微分方程的基质值指数积分方程中起着至关重要的作用，在大规模刚性矩阵微分方程中，（近似）溶液的溶液为低等级。所提出的方法采用缩放和递归过程，采用了级别和递归程序，并由准贝克沃德误差分析来互补，以确定最佳参数。计算成本主要取决于用块向量的稀疏矩阵乘法。数值实验验证了所提出的方法作为矩阵值指数积分器在求解差异Lyapunov方程和riccati方程方面的基础工具。
In this work we present a low-rank algorithm for computing low-rank approximations of large-scale Lyapunov operator $φ$-functions. These computations play a crucial role in implementing of matrix-valued exponential integrators for large-scale stiff matrix differential equations, where the (approximate) solutions are of low rank.The proposed method employs a scaling and recursive procedure, complemented by a quasi-backward error analysis to determine the optimal parameters. The computational cost is primarily determined by the multiplication of sparse matrices with block vectors. Numerical experiments validate the effectiveness of the proposed method as a foundational tool for matrix-valued exponential integrators in solving differential Lyapunov equations and Riccati equations.
