A New Iterative Algorithm for Solving a Class of Matrix Nearness Problem. (8th December 2011)

• Record Type: Journal Article
• Authors: Duan Duan, Xuefeng Xuefeng; Li Li, Chunmei Chunmei
• Other Names: Allahviranloo Allahviranloo T. T. Academic Editor.; Eom Eom K. K. Academic Editor.
• Is Part Of: ISRN computational mathematics. Volume 2012(2012)
• Publication Date: 2011-12-08
• Subjects: Numerical analysis -- Periodicals; Mathematics -- Data processing -- Periodicals; Mathematics -- Data processing; Numerical analysis; Electronic journals; Periodicals; 510
• DOI: 10.5402/2012/126908
• Languages: English
• ISSNs: 2090-7842

Abstract

Abstract : Based on the alternating projection algorithm, which was proposed by Von Neumann to treat the problem of finding the projection of a given point onto the intersection of two closed subspaces, we propose a new iterative algorithm to solve the matrix nearness problem associated with the matrix equations A X B = E, C X D = F, which arises frequently in experimental design. If we choose the initial iterative matrix X 0 = 0, the least Frobenius norm solution of these matrix equations is obtained. Numerical examples show that the new algorithm is feasible and effective.