A collocation procedure is developed for the linear and nonlinear Volterra integral equations, using the globally defined Sinc and auxiliary basis functions. We analytically show the exponential convergence of the Sinc collocation method for approximate solution of Volterra integral equations. Numerical examples are included to confirm applicability and justify rapid convergence of our method.

In this paper we address convergence issues of the Diluted RρR algorithm [1], used to obtain the maximum likelihood estimate to the density matrix in quantum state tomography. We give a new interpretation to the diluted RρR iterations that allows us to prove the global convergence under weaker assumptions. Thus, we propose a new algorithm which is globally convergent and suitable for practical ...

This paper studies the global output convergence of a class of recurrent neural networks with globally Lipschitz continuous and monotone nondecreasing activation functions and locally Lipschitz continuous time-varying inputs. We establish two sufficient conditions for global output convergence of this class of neural networks. Symmetry in the connection weight matrix is not required in the pres...

Banach’s fixed point theorem for contraction maps has been widely used to analyze the convergence of iterative methods in non-convex problems. It is a common experience, however, that iterative maps fail to be globally contracting under the natural metric in their domain, making the applicability of Banach’s theorem limited. We explore how generally we can apply Banach’s fixed point theorem to ...

In this paper, we analyze the stability and convergence of a one-layer neural network proposed by Gao and Wang, which is designed to solve a class of horizontal linear complementarity problems. The globally asymptotical stability and globally exponential stability of this network are proved strictly under mild conditions, respectively. Meanwhile, this network is applied to solve a transportatio...

norwegian university of science and technology trondheim, norway A globally convergent numerical method for a multidimensional Coefficient Inverse Problem for a hyperbolic equation is presented. The global convergence is analytically established. It is shown that this technique provides a good first guess for the adaptivity method, which entails to a synthesis of both approaches. Numerical resu...

In this paper, an algorithm for dynamic rigid-body model is considered. To this end, we first develop an equivalent reformulation of the problem via the Fischer function. Based on this, we propose a new type of method for solving the problem, and the algorithm is shown to be globally convergent and quadratically convergent without nondegenerate assumption. Keywordsdynamic rigid-body model; line...

Local convergence of an inexact-restoration method for nonlinear programming is proved. Numerical experiments are performed with the objective of evaluating the behavior of the purely local method against a globally convergent nonlinear-programming algorithm.

Local convergence of an Inexact-Restoration method for nonlinear programming is proved. Numerical experiments are performed with the objective of evaluating the behavior of the purely local method against a globally convergent nonlinearprogramming algorithm.