It is shown that, under appropriate assumptions, the continuous algebraic Riccati equation with Toeplitz matrices as coefficients has Toeplitz-like solutions. Both infinite and sequences of finite Toeplitz matrices are considered, and also studied is the finite section method, which consists in approximating infinite systems by large finite truncations. The results are proved by translating the...

In this paper we present some results on the dispersionless limit of the Toda lattice equations viewed as the semiclassical limit of an equation involving certain Toeplitz operators. We consider both nonperiodic and periodic boundary conditions. For the nonperiodic case the phase space is the Riemann sphere, while in the periodic case it is the torus C/Z2. In both cases we prove precise estimat...

We propose an algorithm for solving the inverse eigenvalue problem for real symmetric block Toeplitz matrices with symmetric Toeplitz blocks. It is based upon an algorithm which has been used before by others to solve the inverse eigenvalue problem for general real symmetric matrices and also for Toeplitz matrices. First we expose the structure of the eigenvectors of the so-called generalized c...

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 ...

This work considers the problem of constructing efficient MDS matrices over the field F2m . Efficiency is measured by the metric XOR count which was introduced by Khoo et al. in CHES 2014. Recently Sarkar and Syed (ToSC Vol. 1, 2016) have shown the existence of 4 × 4 Toeplitz MDS matrices with optimal XOR counts. In this paper, we present some characterizations of Toeplitz matrices in light of ...

It is shown that, under appropriate assumptions, the continuous algebraic Riccati equation with Toeplitz matrices as coefficients has Toeplitz-like solutions. Both infinite and sequences of finite Toeplitz matrices are considered, and also studied is the finite section method, which consists in approximating infinite systems by large finite truncations. The results are proved by translating the...

In this paper, we give a weakly stable algorithm to solve a block Toeplitz system of linear equations. If the \look-ahead" steps taken to compute the parameters of the inversion formula for the block Toeplitz matrix are small compared to the order n of the matrix, the algorithm requires O(n 2) oating point operations. The parameters of the inversion formula are interpreted and computed in a rec...

We present a fast 5D (frequency and 4 spatial axes) reconstruction method that uses Multichannel Singular Spectrum Analysis / Cazdow algorithm. Rather than embedding the 4D spatial volume in a Hankel matrix, we propose to embed the data into a block Toeplitz form. Rank reduction is carried out via Lanczos bidiagonalization with fast block Toeplitz matrix-times-vector multiplications via 4D Fast...

We propose an adaptation of the partitioning method for determination of the Moore–Penrose inverse of a matrix augmented by a block-column matrix. A simplified implementation of the partitioning method on specific Toeplitz matrices is obtained. The idea for observing this type of Toeplitz matrices lies in the fact that they appear in the linear motion blur models in which blurring matrices (rep...