Fast 0(n2) implementation of Gaussian elimination with partial pivoting is designed for matrices possessing Cauchy-like displacement structure. We show how Toeplitz-like, Toeplitz-plus-Hankel-like and Vandermondelike matrices can be transformed into Cauchy-like matrices by using Discrete Fourier, Cosine or Sine Transform matrices. In particular this allows us to propose a new fast 0{n2) Toeplit...

In this paper we completely characterize compact Toeplitz operators on the harmonic Bergman space. By using this result we establish the short exact sequences associated with the Toeplitz algebra and the Hankel algebra. We show that the Fredholm index of each Fredholm operator in the Toeplitz algebra or the Hankel algebra is zero.  2002 Elsevier Science (USA). All rights reserved.

We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that RR is close to AA. Thus, when the algorithm is used to solve the semi-normal equations RRx = A b, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear systemAx = b. The algorithm also applies to the solution of the full-rank Toeplitz ...

A general scheme is proposed for computing the QR-factorization of certain displacement structured matrices, including Cauchy-like, Vandermonde-like, Toeplitz-like and Hankel-like matrices, hereby extending some earlier work for the QR-factorization of the Cauchy matrix. The algorithm employs a chasing scheme for the recursive construction of a diagonal plus semiseparable matrix of semiseparabi...

In this paper, we consider the robust stabilization problem for linear time varying (LTV) systems using the gap metric. In particular, we show that the time varying (TV) directed gap reduces to an operator with a TV Hankel plus Toeplitz structure. Computation of the norm of such an operator can be carried out using an iterative scheme involving a TV Hankel operator defined on a space of Hilbert...

New generalized split Levinson and Schur algorithms for the two-dimensional linear least squares prediction problem on a polar raster are derived. The algorithms compute the prediction filter for estimating a random field at the edge of a disk, from noisy observations inside the disk. The covariance function of the random field is assumed to have a Toeplitzplus-Hankel structure for both its rad...

An exact formula was recently obtained for the spectral norms of the Lucas and Fibonacci Hankel matrices [1], and also for the Lucas and Fibonacci Toeplitz matrices [4]. These results put finishing touches on the works initiated in [2] and [3]. On another front, bounds were found for the spectral norms of k-Fibonacci and k-Lucas Toeplitz matrices [7]. In this paper, we present the exact value f...

We present new fast algorithms for solving the Toeplitz and the Toeplitz-plus-Hankel least squares problems. These algorithms are based on a new fast algorithm for solving the Cauchy-like least squares problem. We perform an error analysis and provide conditions under which these algorithms are numerically stable. We also develop implementation techniques that signiicantly reduce the execution ...