A Fast α-circulant Absolute Value Preconditioner for All-at-once Systems from Wave Equations
In order to accelerate convergence rate of the preconditioned MINRES method for all-at-once systems from wave equations,we propose a new α-circulant absolute value preconditioner based on the absolute value preconditioners and the block tridiagonal Toeplitz preconditioners.Fur-thermore,we prove that the corresponding preconditioned matrix can be approximately split into the sum of the orthogonal matrix and the low-rank matrix,and its eigenvalues are clustered around±1,which leads to fast convergence rate of the preconditioned MINRES method.Numerical results also demonstrate the effectiveness of the new preconditioner.
wave equationsall-at-once systemspreconditioned MINRES methodα-circulant ab-solute value preconditioner
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