Abstract
We provide effective algorithms for solving block tridiagonal block Toeplitz systems with m×m quasiseparable blocks, as well as quadratic matrix equations with m×m quasiseparable coefficients, based on cyclic reduction and on the technology of rank-structured matrices. The algorithms rely on the exponential decay of the singular values of the off-diagonal submatrices generated by cyclic reduction. We provide a formal proof of this decay in the Markovian framework. The results of the numerical experiments that we report confirm a significant speed up over the general algorithms, already starting with the moderately small size m≈102.
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