Fast superoptimal preconditioning of multiindex Toeplitz matrices

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Abstract

In this article three well-known methods of circulant preconditioning of finite multiindex Toeplitz linear systems, that is linear systems indexed by integers i1, ..., id with 0 ≤ is < ns (s = 1, ..., d), are studied in detail. A general algorithm for the construction of the so-called superoptimal preconditioner is also given and it is shown that this procedure requires O(n1 ⋯ ndlog(n1 ⋯ nd)) floating point operations. © 2006 Elsevier Inc. All rights reserved.

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van der Mee, C., Rodriguez, G., & Seatzu, S. (2006). Fast superoptimal preconditioning of multiindex Toeplitz matrices. Linear Algebra and Its Applications, 418(2–3), 576–590. https://doi.org/10.1016/j.laa.2006.02.034

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