Anderson(m) is a method for acceleration of fixed point iteration which stores m + 1 prior evaluations of the fixed point map and computes the new iteration as a linear combination of those evaluations. Anderson(0) is fixed point iteration. In this paper we show that Anderson(m) is locally r-linearly convergent if the fixed point map is a contraction and the coefficients in the linear combinati...

The FastICA algorithm can be considered as a selfmap on a manifold. It turns out that FastICA is a scalar shifted version of an algorithm recently proposed. We put these algorithms into a dynamical system framework. The local convergence properties are investigated subject to an ideal ICA model. The analysis is very similar to the wellknown case in numerical linear algebra when studying power i...

0. Systems theory I. Part 1: Convergence A. Two approaches to convergence B. A mathematical formulation of convergence C. Convergence is a Markov process D. Starting configuration doesn’t matter II. Part 2: Analysis A. Background and mathematical foundation 1. Stochastic matrices 2. The Eigenvalue problem 3. Spectral Decomposition 4. Spectral Decomposition of M B. The Algebraic View 1. Partitio...

The paper discusses the impact and implications of Korean unification by setting up a two-region endogenous growth model. The numerical solutions are based on the formal analytical model, and have been calibrated so that they reflect the observed features of the North and South Korean economies. The numerical solutions provide evidence about the speed of convergence and the large amount of inte...

Determining when a numerical simulation is fully converged is important in getting accurate and reliable results. In this study a new convergence criterion based on extracting the energetic modes of a numerical solution, based on the Proper Orthogonal Decomposition method, is suggested. The POD convergence criterion is tested and applied to flow over a bluff body which has been solved numerical...

The purpose of this paper is to provide the convergence theory for the iterative approach given by Chu [SIAM J. Numer. Anal.,29 (1992), pp. 885–903] in the context of solving inverse singular value problems. We give a detailed convergence analysis and investigate the ultimate rate of convergence. Numerical results which confirm our theory are presented.

This paper investigates the convergence of the Lanczos method for computing the smallest eigenpair of a selfadjoint elliptic diierential operator via inverse iteration (without shifts). Superlinear convergence rates are established, and their sharpness is investigated for a simple model problem. These results are illustrated numerically for a more diicult problem.

A synthesis of a globally convergent numerical method for a coefficient inverse problem and the adaptivity technique is presented. First, the globally convergent method provides a good approximation for the unknown coefficient. Next, this approximation is refined via the adaptivity technique. The analytical effort is focused on a posteriori error estimates for the adaptivity. A numerical test i...

a systematic way is presented for the construction of multi-step iterative method with frozen jacobian. the inclusion of an auxiliary function is discussed. the presented analysis shows that how to incorporate auxiliary function in a way that we can keep the order of convergence and computational cost of newton multi-step method. the auxiliary function provides us the way to overcome the singul...