Lower bound for the convergence rate of nonstationary Jacobi-like iteration

Stationary and nonstationary Jacobi-like iterative processes for solving systems of linear algebraic equations are examined. For a system whose coefficient matrix A is an H-matrix, it is shown that the convergence rate of any Jacobi-like process is at least as high as that of the point Jacobi method as applied to a system with 〈A〉 as the coefficient matrix, where 〈A〉 is a comparison matrix of A.     

Approximate Inverse Preconditioners for Some Large Dense Random Electrostatic Interaction Matrices

A sparse mesh-neighbour based approximate inverse preconditioner is proposed for a type of dense matrices whose entries come from the evaluation of a slowly decaying free space Green’s function at randomly placed points in a unit cell. By approximating distant potential fields originating at closely spaced sources in a certain way, the preconditioner is given properties similar to, or better than, those of a standard least squares approximate inverse preconditioner while its setup cost is only that of a diagonal block approximate inverse preconditioner. Numerical experiments on iterative solutions of linear systems with up to four million unknowns illustrate how the new preconditioner drastically outperforms standard approximate inverse preconditioners of otherwise similar construction, and especially so when the preconditioners are very sparse. AMS subject classification (2000) 65F10, 65R20, 65F35, 78A30     

Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models

This paper proposes a new method that extends the efficient global optimization to address stochastic black-box systems. The method is based on a kriging meta-model that provides a global prediction of the objective values and a measure of prediction uncertainty at every point. The criterion for the infill sample selection is an augmented expected improvement function with desirable properties for stochastic responses. The method is empirically compared with the revised simplex search, the simultaneous perturbation stochastic approximation, and the DIRECT methods using six test problems from the literature. An application case study on an inventory system is also documented. The results suggest that the proposed method has excellent consistency and efficiency in finding global optimal solutions, and is particularly useful for expensive systems.     

Decision methods for linearly ordered Heyting algebras

The decision problem for positively quantified formulae in the theory of linearly ordered Heyting algebras is known, as a special case of work of Kreisel, to be solvable; a simple solution is here presented, inspired by related ideas in Gödel-Dummett logic.     

Some Notes on the Linear Complexity of Sidel’nikov-Lempel-Cohn-Eastman Sequences

We continue the study of the linear complexity of binary sequences, independently introduced by Sidel’nikov and Lempel, Cohn, and Eastman. These investigations were originated by Helleseth and Yang and extended by Kyureghyan and Pott. We determine the exact linear complexity of several families of these sequences using well-known results on cyclotomic numbers. Moreover, we prove a general lower bound on the linear complexity profile for all of these sequences.     

电磁散射问题手性障碍边界重构的线性探测法的理论分析

In this paper,we consider the inverse scattering by chiral obstacle inelectromagnetic fields,and prove that the linear sampling method is also effective todetermine the support of a chiral obstacle from the noisy far field data.     

A posteriori error estimates of discontinuous Galerkin methods for non-standard Volterra integro-differential equations

^** Email: jingtang{at}lsec.cc.ac.cn^*** Email: hermann{at}math.mun.ca In this paper we establish a posteriori error estimates forthe discontinuous Galerkin (DG) method applied to linear, semilinearand non-standard (non-linear) Volterra integro-differentialequations. We also present an analysis of the DG method withquadrature for the memory term. Numerical experiments basedon three integro-differential equations are used to illustratevarious aspects of the error analysis.     

The regulator problem for linear systems with constrained control: an LMI approach

^** Email: benzaouia{at}ucam.ac.ma A new methodology of the partial eigenstructure assignment bystate feedback via linear matrix inequality (LMI) is extendedto obtain a solution of the constrained regulator problem forlinear continuous-time and discrete-time systems by using theLMI formulation.     

On the Linear Complexity Profile of Nonlinear Congruential Pseudorandom Number Generators with Dickson Polynomials

Linear complexity and linear complexity profile are important characteristics of a sequence for applications in cryptography and Monte-Carlo methods. The nonlinear congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation. Recently, a weak lower bound on the linear complexity profile of a general nonlinear congruential pseudorandom number generator was proven by Gutierrez, Shparlinski and the first author. For most nonlinear generators a much stronger lower bound is expected. Here, we obtain a much stronger lower bound on the linear complexity profile of nonlinear congruential pseudorandom number generators with Dickson polynomials.     

Business–Cycle Models and the Dangers of Linearizing

This paper studies the consequences of linearizing nonlinear business–cycle models near their interior steady state. It is shown that dynamic objects, created for example in a Bogdanov-Takens bifurcation, may be lost in the linearization procedure. Sufficient conditions are provided ensuring the absence of various dynamic features in the nonlinear version of the model. The authors thank Andy Atkeson and Hal Cole for useful comments and suggestions. They also thank three anonymous referees who have helped to greatly improve the exposition of this paper. Part of this research was done while the author was affiliated with the University of Cergy Pontoise (THEMA) and during visits at DELTA. Part of this research has been done while the author was working as a Marie Curie Fellow at INSEE/CREST and during visits at the University of Warwick.