Nonsymmetric Algebraic Riccati Equations under the Tensor Product. (26th April 2023)

• Record Type: Journal Article
• Authors: Shao, Xiongyu; Wei, Yimin; Yuan, Jin-Yun
• Is Part Of: Numerical functional analysis and optimization. Volume 44:Number 6(2023)
• Page Start: 545
• Page End: 563
• Publication Date: 2023-04-26
• Subjects: Nonsymmetric algebraic Riccati equation -- T-M-tensor -- the fast Fourier transform T-product; 15A18 -- 15A69 -- 65F15 -- 65F10 -- 90C11; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2023.2192593
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: The nonsymmetric algebraic Riccati equation is proposed by using the tensor product. The existence of its minimal nonnegative solution is studied. The sufficient condition of the existence and the uniqueness of the minimal nonnegative solution is given by M -tensor as well. The solution can be obtained by the fast Fourier transform which save computational cost of computing the required solution. Some numerical experiments are performed.