Concurrent iterative algorithm for Toeplitz-like linear systems
- 1 May 1993
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Parallel and Distributed Systems
- Vol. 4 (5) , 592-600
- https://doi.org/10.1109/71.224221
Abstract
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.Keywords
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