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Concurrent Iterative Algorithm for Toeplitz-like Linear Systems
May 1993 (vol. 4 no. 5)
pp. 592-600

A nonsingular n*n matrix A is given with its short displacement generator. It has smalldisplacement rank bounded by a fixed constant. The class of such matrices generalizesToeplitz matrices. A good initial approximation to a short displacement generator forA/sup -1/ is readily available. Ways to refine this approximation and numerically compute a displacement generator of A/sup -1/ and the solution vector x=A/sup -1/b to a linear system Ax=b by using O(log/sup 2/n) parallel arithmetic steps and n processors arepresented. These results are extended to some other important classes of densestructure matrices.

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Index Terms:
Index Termsparallel algorithm; iterative algorithm; Toeplitz-like linear systems; parallel arithmeticsteps; computational complexity; matrix algebra; parallel algorithms
Citation:
V.Y. Pan, "Concurrent Iterative Algorithm for Toeplitz-like Linear Systems," IEEE Transactions on Parallel and Distributed Systems, vol. 4, no. 5, pp. 592-600, May 1993, doi:10.1109/71.224221
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