Abstract Stationary splitting iterative methods for solving A X B = C are considered in this paper. The main tool to derive our new method is the induced splitting of a given nonsingular matrix A = M − N by a matrix H such that ( I − H ) − 1 exists. Convergence properties of the proposed method are discussed and numerical experiments are presented to illustrate its computational efficiency and the effectiveness of some preconditioned variants. In particular, for certain surface fitting applications our method is much more efficient than the progressive iterative approximation (PIA), a conventional iterative method often used in computer aided geometric design (CAGD).

中文翻译：

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矩阵方程AXB=C的平稳分裂迭代法

摘要 本文考虑了求解AXB = C的平稳分裂迭代法。推导出我们的新方法的主要工具是给定的非奇异矩阵 A = M − N 被矩阵 H 诱导分裂，使得 ( I − H ) − 1 存在。讨论了所提出方法的收敛特性，并提出了数值实验来说明其计算效率和一些预处理变体的有效性。特别是，对于某些表面拟合应用，我们的方法比渐进迭代近似 (PIA) 高效得多，这是一种常用于计算机辅助几何设计 (CAGD) 的传统迭代方法。