The computation of the square roots of circulant matrices

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• 作者：Chengbo Lu^a ; ^b ; Chuanqing Gu^a ; ^{cqgu@staff.shu.edu.cn}
• 关键词：Circulant matrix ; Quasi-skew circulant matrix ; Principal square root ; Reduced form ; H-matrix ; M-matrix ; Schur decomposition
• 刊名：Applied Mathematics and Computation
• 出版年：2011
• 出版时间：15 April 2011
• 年：2011
• 卷：217
• 期：16
• 页码：6819-6829
• 全文大小：233 K

文摘

In the first part of this paper, we investigate the reduced forms of circulant matrices and quasi-skew circulant matrices. By using their properties we present two efficient algorithms to compute the square roots of circulant matrices and quasi-skew circulant matrices, respectively. Those methods are faster than the traditional algorithm which is based on the Schur decomposition. In the second part, we further consider circulant H-matrices with positive diagonal entries and develop two algorithms for computing their principal square roots. Those two algorithms have the common advantage that is they only need matrix–matrix multiplications in their iterative sequences, an operation which can be done very efficiently on modern high performance computers.