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- Title
Lanczos version of BCR algorithm for solving the generalised second-order Sylvester matrix equation EVF + GVH + BVC = DWE + M.
- Authors
Hajarian, Masoud
- Abstract
It is well known that the biconjugate residual (BCR) algorithm and its variants are powerful procedures to find the solution of large sparse non-symmetric systems equation Ax = b. In this study, the authors develop the Lanczos version of BCR algorithm for computing the solution pair (V, W ) of the generalised second-order Sylvester matrix equation EVF + GVH + BVC = DWE + M, which includes the second-order Sylvester, Lyapunov and Stein matrix equations as special cases. The convergence results show that the algorithm with any initial matrices converges to the solutions within a finite number of iterations in the absence of round-off errors. Finally, two numerical examples are provided to support the theoretical findings and to testify the effectiveness and usefulness of the algorithm.
- Subjects
ALGORITHMS; SYLVESTER matrix equations; NEWTON-Raphson method; MATLAB (Computer software); MATHEMATICS theorems
- Publication
IET Control Theory & Applications (Wiley-Blackwell), 2017, Vol 11, Issue 2, p273
- ISSN
1751-8644
- Publication type
Article
- DOI
10.1049/iet-cta.2016.0658