论文标题
矩阵方程，稀疏求解器：M-M.E.S.S.-2.0.1-哲学，功能和应用（参数）模型
Matrix Equations, Sparse Solvers: M-M.E.S.S.-2.0.1 -- Philosophy, Features and Application for (Parametric) Model
论文作者
论文摘要
矩阵方程在（数值）线性代数和系统理论中无处不在。尤其是在模型顺序降低（MOR）中，它们在许多基于平衡的还原方法的线性动力学系统中起着关键作用。当这些系统来自进化部分偏微分方程的空间离散化时，它们的系数矩阵通常很大且稀疏。此外，这些系统的输入和输出数量通常远小于空间自由度的数量。然后，在许多情况下，都观察到相应的大规模矩阵方程的解为低（数值）等级。此功能由M-M.E.S.S利用。为了找到近似近似溶液的较大的低级因数化。这项贡献描述了包装的实现和功能背后的基本理念，以及其在模型顺序减少大规模线性时间不变（LTI）系统和参数LTI系统中的应用。
Matrix equations are omnipresent in (numerical) linear algebra and systems theory. Especially in model order reduction (MOR) they play a key role in many balancing based reduction methods for linear dynamical systems. When these systems arise from spatial discretizations of evolutionary partial differential equations, their coefficient matrices are typically large and sparse. Moreover, the numbers of inputs and outputs of these systems are typically far smaller than the number of spatial degrees of freedom. Then, in many situations the solutions of the corresponding large-scale matrix equations are observed to have low (numerical) rank. This feature is exploited by M-M.E.S.S. to find successively larger low-rank factorizations approximating the solutions. This contribution describes the basic philosophy behind the implementation and the features of the package, as well as its application in the model order reduction of large-scale linear time-invariant (LTI) systems and parametric LTI systems.
