Matrix form of the Bi‐CGSTAB method for solving the coupled Sylvester matrix equations | Zendy

Hajarian Masoud | Zendy

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Matrix 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 , sylvester matrix , sylvester's law of inertia , matrix (chemical analysis) , mathematics , control theory (sociology) , symmetric matrix , computer science , mathematical analysis , physics , artificial intelligence , control (management) , materials science , polynomial matrix , eigenvalues and eigenvectors , matrix polynomial , quantum mechanics , 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.

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