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An Iterative-Improvement Approach to the Numerical Solution of Vector Toeplitz Systems
March 1974 (vol. 23 no. 3)
pp. 320-325
M.P. Ekstorm, Electrical Engineering Department, Lawrence Livermore Laboratory, University of California
This paper describes an algorithm for the approximate solution of vector Toeplitz systems via an iterative-improvement method. The algorithm exploits the special structure of Toeplitz matrices, namely, their similarity to vector circulants, and is particularly well suited for solving large systems. Sufficient convergence conditions and concrete error bounds for the iteration are presented along with an application of the routine to a problem in the design of planar digital filters for image processing.
Index Terms:
Finite Fourier transform (fFT), linear systems of equations, matrix inversion, vector-Toeplitz matrix, vector-circulant matrix.
Citation:
M.P. Ekstorm, "An Iterative-Improvement Approach to the Numerical Solution of Vector Toeplitz Systems," IEEE Transactions on Computers, vol. 23, no. 3, pp. 320-325, March 1974, doi:10.1109/T-C.1974.223929
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