Toeplitz matrix

An adaptive disturbance rejection algorithm is developed for the standard control problem. The MIMO system and controller are represented as ARMARKOV/Toeplitz models, and the parameter matrix of the compensator is updated online by means of a gradient algorithm. The algorithm requires minimal knowledge of the plant, specifically, the numerator of the ARMARKOV transfer function from control to performance is required. No knowledge about the spectrum of the disturbance is needed. Experimental results demonstrating tonal and broadband disturbance rejection in an acoustic duct are presented

This paper studies the application of preconditioned conjugate gradient methods in high resolution image reconstruction problems. We consider reconstructing high resolution images from multiple undersampled, shifted, degraded frames with subpixel displacement errors. The resulting blurring matrices are spatially variant. The classical Tikhonov regularization and the Neumann boundary condition are used in the reconstruction process. The preconditioners are derived by taking the cosine transform approximation of the blurring matrices. We prove that when the or norm regularization functional is used, the spectra of the preconditioned normal systems are clustered around 1 for sufficiently small subpixel displacement errors. Conjugate gradient methods will hence converge very quickly when applied to solving these preconditioned normal equations. Numerical examples are given to illustrate the fast convergence.

In this paper, we study the problem of reconstructing a high-resolution image from several blurred low-resolution image frames. The image frames consist of decimated, blurred and noisy versions of the high-resolution image. The high-resolution image is modeled as a Markov random field (MRF), and a maximum a posteriori (MAP) estimation technique is used for the restoration. We show that with the periodic boundary condition, the high-resolution image can be restored efficiently by using fast Fourier transforms. We also apply the preconditioned conjugate gradient method to restore the high-resolution image. Computer simulations are given to illustrate the effectiveness of the proposed method.

This paper presents a parallel algorithm to solve a structured linear system with a symmetric-Toeplitz matrix. Our main result concerns the use of a combination of shared and distributed memory programming tools to obtain a multilevel algorithm that exploits the actual different hierarchical levels of memory and computational units present in parallel architectures. This gives, as a result, a so-called parallel hybrid algorithm that is able to exploit each of these different configurations. Our approach has been done not only by means of combining standard implementation tools like OpenMP and MPI, but performing the appropriate mathematical derivation that allows this derivation. The experimental results over different representations of available parallel hardware configurations show the usefulness of our proposal.