Computing symmetric solutions of general Sylvester matrix equations via Lanczos version of biconjugate residual algorithm. (15th August 2018)

• Record Type: Journal Article
• Authors: Hajarian, Masoud
• Is Part Of: Computers & mathematics with applications. Volume 76:issue 4(2018)
• Page Start: 686
• Page End: 700
• Publication Date: 2018-08-15
• Subjects: Lanczos version of biconjugate residual (BCR) algorithm -- Symmetric solution -- General Sylvester matrix equations; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.05.010
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: Many problems in control theory can be studied by obtaining the symmetric solution of linear matrix equations. In this investigation, we deal with the symmetric solutions X, Y and Z of the general Sylvester matrix equations A 1 X B 1 + C 1 Y D 1 + E 1 Z F 1 = G 1, A 2 X B 2 + C 2 Y D 2 + E 2 Z F 2 = G 2, ⋮ ⋮ ⋮ ⋮ A t X B t + C t Y D t + E t Z F t = G t . The Lanczos version of biconjugate residual (BCR) algorithm is generalized to compute the symmetric solutions of the general Sylvester matrix equations. The convergence properties of this algorithm are discussed and it is proven that it smoothly converges to the symmetric solutions of the general Sylvester matrix equations in a finite number of iterations in the absence of round-off errors. Finally, the comparative numerical results are carried out to support that the current algorithm may be more efficient than other iterative algorithms.