Open AccessMatrix form of the Bi‐CGSTAB method for solving the coupled Sylvester matrix equations
Author(s) -
Hajarian Masoud
Publication year - 2013
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2013.0101
Subject(s) - sylvester equation , kronecker product , sylvester matrix , matrix (chemical analysis) , hermitian matrix , conjugate gradient method , mathematics , sylvester's law of inertia , symmetric matrix , algebra over a field , computer science , mathematical optimization , mathematical analysis , kronecker delta , pure mathematics , eigenvalues and eigenvectors , physics , materials science , matrix polynomial , quantum mechanics , polynomial matrix , polynomial , composite material
The bi‐conjugate gradient stabilised (Bi‐CGSTAB) method is one of the efficient computational tools to solve the non‐Hermitian linear systems Ax = b . By employing Kronecker product and vectorisation operator, this study investigates the matrix form of the Bi‐CGSTAB method for solving the coupled Sylvester matrix equations ∑ i =1 k ( A i XB i + C i YD i ) = M , ∑ i =1 k ( E i XF i + G i YH i ) = N [including (second‐order) Sylvester and Lyapunov matrix equations as special cases] encountered in many systems and control applications. Several numerical examples are given to compare the efficiency and performance of the investigated method with some existing algorithms.