Abstract
We present a parallel algorithm which computes recursively, in increasing order, the complete generalized eigendecompositions of the successive subpencils contained in a maximum size Hermitian Toeplitz generalized eigenproblem. At each order a number of independent, structurally identical, nonlinear problems are solved in parallel, facilitating fast implementation. The multiple and clustered minimum eigenvalue cases are treated in detail. In the application of our algorithm to narrowband array processing in colored noise, the direction-of-arrival containing eigenspace information is provided recursively in order. This permits estimation of the angles of arrival for subsequent orders, facilitating early estimation of the number of sources as well as verification of results obtained at previous orders.
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This research was supported in part by the Center for Innovative Technology Grant No. INF-86-018, Herndon, Virginia, and Unisys Corporation, Grant No. V120483, Reston, Virginia.
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Fargues, M.P., (Louis) Beex, A.A. Fast order-recursive generalized Hermitian Toeplitz eigenspace decomposition. Math. Control Signal Systems 4, 99–117 (1991). https://doi.org/10.1007/BF02551383
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DOI: https://doi.org/10.1007/BF02551383