Mastronardi, Lemmerling, and van Huffel presented an algorithm
for solving a total least squares problem when the matrix
and its perturbations are Toeplitz. A Toeplitz matrix is a
special kind of matrix with small displacement rank. Here we
generalize the fast algorithm to any matrix with small displacement
rank. In particular, we show how to efficiently construct the
generators whenever M has small displacement rank and show that
in many important cases the Cholesky factorization of the matrix
MTM can also be determined fast. We further extend this problem
to Tikhonov regularization of ill-posed problems and illustrate the
use of the algorithm on an image deblurring problem.
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