A method of computing an inversion (X) of a nearly Toeplitz n by n matrix (A). A perturbation matrix (E) is first determined such that the sum of the nearly Toeplitz matrix (A) and the perturbation matrix (E) is a Toeplitz matrix (T). The inversion is solved by solving the equation X=T.sup.-1(B+EX), where B is a vector or matrix of dimension n by m. An initial estimate X.sup.(0) is selected and estimates of the inversion X are iteratively computed through the recursion X.sup.(n-1)=T.sup.-1(B+EX.sup.(n)). The initial estimate X.sup.(0) may be equal to an inversion (T.sup.-1) of the Toeplitz matrix (T). The present invention may be utilized in a radio receiver to efficiently compute (1) a least-squares (LS) channel estimate, (2) minimum mean squared error (MMSE) prefilter coefficients for a decision feedback equalizer (DFE), or (3) an autoregressive (AR) noise-spectrum estimation from a finite number of observed noise samples.