In this article three well-known methods of circulant preconditioning of finite multiindex Toeplitz linear systems, that is linear systems indexed by integers i1, ..., idwith 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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