本文讨論了矩陣值函數有理逼近的幾種算法，包括插值AAA法、基于近似最小二乘拟合的RKFIT法、向量拟合的RKFIT法和基于塊Loewner矩陣低秩逼近的RKFIT法。本文提出了一種基于帶矩陣權值的廣義重心公式的塊- AAA算法。對模型降階問題和非線性特征值問題，包括有噪聲資料的例子，從近似精度和運作時間兩方面對所有算法進行了比較。研究發現，基于插值的方法通常運作成本較低，但在存在噪聲的情況下會受到影響，而基于近似的方法性能更好。
原文題目：Algorithms for the rational approximation of matrix-valued functions
原文：A selection of algorithms for the rational approximation of matrix-valued functions are discussed, including variants of the interpolatory AAA method, the RKFIT method based on approximate least squares fitting, vector fitting, and a method based on low-rank approximation of a block Loewner matrix. A new method, called the block-AAA algorithm, based on a generalized barycentric formula with matrix-valued weights is proposed. All algorithms are compared in terms of obtained approximation accuracy and runtime on a set of problems from model order reduction and nonlinear eigenvalue problems, including examples with noisy data. It is found that interpolation-based methods are typically cheaper to run, but they may suffer in the presence of noise for which approximation-based methods perform better.
原文作者：Ion Victor Gosea, Stefan Güttel
原文位址：https://arxiv.org/abs/2003.06410
矩陣值函數的有理逼近算法（CS NA）.pdf