Search

Abstract: We consider the iterative solution of unconstrained minimization problems arising from nonlinear image restoration. Our approach is based on a novel generalized BFGS method for such large-scale image restoration minimization problems. The complexity per step of the method is of operations and only memory allocations are required, where is the number of image pixels. Based on the results given in [Carmine Di Fiore, Stefano Fanelli, Filomena Lepore, Paolo Zellini, Matrix algebras in quasi-Newton methods for unconstrained minimization, Numer. Math. 94 (2003) 479–500], we show that the method is globally convergent for our nonlinear image restoration problems. Experimental results are presented to illustrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

We study efficient iterative methods for Toeplitz systems based on the circulant and skew-circulant splitting (CSCS) of the Toeplitz matrix. Theoretical analysis show that if the circulant and the skew-circulant splitting matrices are positive definite, then the CSCS method converges to the unique solution of the system of linear equations. Moreover, we derive an upper bound of the contraction factor of the CSCS iteration which is dependent solely on the spectra of the circulant and the skew-circulant matrices involved. Numerical examples are presented to demonstrate the method. [Copyright &y& Elsevier]

We consider the system of equations arising from finite difference discretization of a three-dimensional convection–diffusion model problem. This system is typically nonsymmetric. The GMRES method with the Strang block-circulant preconditioner is proposed for solving this linear system. We show that our preconditioners are invertible and study the spectra of the preconditioned matrices. Numerical results are reported to illustrate the effectiveness of our methods. [Copyright &y& Elsevier]

In this paper, we study and analyze absolute and relative condition numbers of the spectral projections for regular periodic eigenproblems. The main contribution is to derive explicit expressions of the condition numbers of the j-th left and right spectral projections. Numerical examples are given to illustrate the proposed condition numbers for the spectral projections associated with periodic eigenproblems. [ABSTRACT FROM AUTHOR]

Abstract: Given a Probabilistic Boolean Network (PBN), an important problem is to study its steady-state probability distribution for network analysis. In this paper, we present a new perturbation bound of the steady-state probability distribution of PBNs with gene perturbation. The main contribution of our results is that this new bound is established without additional condition required by the existing method. The other contribution of this paper is to propose a fast algorithm based on the special structure of a transition probability matrix of PBNs with gene perturbation to compute its steady-state probability distribution. Experimental results are given to demonstrate the effectiveness of the new bound, and the efficiency of the proposed method. [Copyright &y& Elsevier]