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\begin{document}

\title{On the solution of the distributed optimal control problem with
time-periodic parabolic equations}



\author[1]{Davod Khojasteh  Salkuyeh }%
\affil[1]{University of Guilan}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\begin{abstract}
We consider the system of linear equations arisen from the finite
element discretization of the distributed optimal control problem with
time-periodic parabolic equations. A block alternating splitting
iteration (BASI) method is presented for solving the obtained system. We
prove that the BASI method is unconditionally convergent. We derive the
BASI preconditioner and present an estimation formula for the parameter
of the BASI preconditioner. Numerical results are presented to verify
the efficiency of both the BASI method and the BASI preconditioner.
Comparison with some existing methods are also given.%
\end{abstract}%



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