We consider exponentially weighted reeursive least squares (RLS) computations with forgetting factor 3/ (0 < 3' < 1). The least squares estimator can be found by solving a matrix system A(t)x(t)= b(t) at each adaptive time step t. Unlike the sliding window RLS computation, the matrix A(t) is not a "near-Toeplitz" matrix (a sum of products of Toeplitz matrices). However, we show that its sealed matrix is a "near-Toeplitz" matrix, and hence the matrix-vector multiplication can be performed efficiently by using fast Fourier transforms (FFTs). We apply the FFT-based preconditioned conjugate gradient method to solve such systems. When the input stochastic process is stationary, we prove that both 8"IliA(t) -E(A(t))II~] and Var[llA(t) -E( A(t))ll2] tend to zero, provided that the number of data samples taken is sufficient large. Here g'(') and Var(-) are the expectation and variance operators respectively. Hence the expected values of the eigenvalues of the preconditioned matrices are near to 1 except for a finite number of outlying eigenvalues. The result is stronger than those proved by Ng, Chan, and Plemmons that the spectra of the preconditioned matrices are clustered around 1 with probability 1.