Convergence criterion of Newton's method for singular systems with constant rank derivatives

AbstractThe present paper is concerned with the convergence problem of Newton's method to solve singular systems of equations with constant rank derivatives. Under the hypothesis that the derivatives satisfy a type of weak Lipschitz condition, a convergence criterion based on the information around the initial point is established for Newton's method for singular systems of equations with constant rank derivatives. Applications to two special and important cases: the classical Lipschitz condition and the Smale's assumption, are provided; the latter, in particular, extends and improves the corresponding result due to Dedieu and Kim in [J.P. Dedieu, M. Kim, Newton's method for analytic systems of equations with constant rank derivatives, J. Complexity 18 (2002) 187–209]

Convergence Behavior for Newton-Steffensen’s Method under -Condition of Second Derivative

The present paper is concerned with the semilocal as well as the local convergence problems of Newton-Steffensen’s method to solve nonlinear operator equations in Banach spaces. Under the assumption that the second derivative of the operator satisfies -condition, the convergence criterion and convergence ball for Newton-Steffensen’s method are established

Semilocal Convergence Analysis for Inexact Newton Method under Weak Condition

Under the hypothesis that the first derivative satisfies some kind of weak Lipschitz conditions, a new semilocal convergence theorem for inexact Newton method is presented. Unified convergence criteria ensuring the convergence of inexact Newton method are also established. Applications to some special cases such as the Kantorovich type conditions and γ-Conditions are provided and some well-known convergence theorems for Newton's method are obtained as corollaries

Analysis of Minimum Numbers of Linearly Active S-Boxes of a Class of Generalized Feistel Block Ciphers

For a class of generalized Feistel block ciphers, an explicit recurrent formula for the minimum numbers of linearly active $S$-boxes of any round $r$ is presented

Drivers of cropland abandonment in mountainous areas: A household decision model on farming scale and a case study of Southwest China

Cropland abandonment has emerged as a prevalent phenomenon in the mountainous areas of China.While there is a general understanding that this new trend is driven by the rising opportunity cost of rural labor, rigorous theoretical and empirical analyses are largely absent. This paper first develops a theoretical model to investigate household decisions on farming scale when off-farm labor market is accessible and there is heterogeneity of farmland productivity and distribution. The model is capable of explaining the hidden reasons of cropland abandonment in sloping and agriculturally less-favored locations. The model also unveils the impacts of heterogeneity of household labor on fallow decisions and the efficiency loss due to an imperfect labor market. The model is empirically tested by applying the Probit and Logit estimators to a unique household and land-plot survey dataset which contains 5258 plots of599 rural households in Chongqing, a provincial level municipality, in Southwest China. The survey shows that more than 30% of the sample plots have been abandoned, mainly since 1992. The econometric results are consistent with our theoretical expectations. This work would help policy-makers and stakeholders to identify areas with a high probability of land abandonment and farming practice which is less sustainable in the mountainous areas

Regularization and Iterative Methods for Monotone Variational Inequalities

We provide a general regularization method for monotone variational inequalities, where the regularizer is a Lipschitz continuous and strongly monotone operator. We also introduce an iterative method as discretization of the regularization method. We prove that both regularization and iterative methods converge in norm

A Globally Convergent Inexact Newton-Like Cayley Transform Method for Inverse Eigenvalue Problems

We propose a inexact Newton method for solving inverse eigenvalue problems (IEP). This method is globalized by employing the classical backtracking techniques. A global convergence analysis of this method is provided and the R-order convergence property is proved under some mild assumptions. Numerical examples demonstrate that the proposed method is very effective for solving the IEP with distinct eigenvalues.Comment: 18 pages, 2 table