Abstract :
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.
Keywords :
Finite Fourier transform (fFT), linear systems of equations, matrix inversion, vector-Toeplitz matrix, vector-circulant matrix.; Convolution; Covariance matrix; Estimation theory; Image restoration; Integral equations; Multidimensional systems; Optical noise; Sparse matrices; Transmission line matrix methods; Vectors; Finite Fourier transform (fFT), linear systems of equations, matrix inversion, vector-Toeplitz matrix, vector-circulant matrix.;
