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Lanczos version of BCR algorithm for solving the generalised second-order Sylvester matrix equation

Lanczos version of BCR algorithm for solving the generalised second-order Sylvester matrix equation

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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 . In this study, the authors develop the Lanczos version of BCR algorithm for computing the solution pair of the generalised second-order Sylvester matrix equationwhich 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.

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