A penalized Fischer-Burmeister NCP-function

We introduce a new NCP-function in order to reformulate the nonlinear complementarity problem as a nonsmooth system of equations. This new NCP-function turns out to have stronger theoretical properties than the widely used Fischer-Burmeister function and other NCP-functions suggested previously. Moreover, numerical experience indicates that a semismooth Newton method based on this new NCP-function performs considerably better than the corresponding method based on the Fischer-Burmeister function. Received: March 10, 1997 / Accepted: February 15, 2000?Published online May 12, 2000     

An L-ribbon for large underdetermined linear discrete ill-posed problems

The L-curve is a popular aid for determining a suitable value of the regularization parameter when solving ill-conditioned linear systems of equations with a right-hand side vector, which is contaminated by errors of unknown size. However, for large problems, the computation of the L-curve can be quite expensive, because the determination of a point on the L-curve requires that both the norm of the regularized approximate solution and the norm of the corresponding residual vector be available. Recently, an approximation of the L-curve, referred to as the L-ribbon, was introduced to address this difficulty. The present paper discusses how to organize the computation of the L-ribbon when the matrix of the linear system of equations has many more columns than rows. Numerical examples include an application to computerized tomography.     

n阶泛函微分方程边值问题

本文研究下列n阶RFDE边值问题:x⁽ⁿ⁾(t)=f(t,x_t,x(t),x′(t),…,x^(n-1)(t)),　t∈［0,T ］,x(t)=φ(t),t∈［-r,0］;x′(0)=η,x″(0)=η₂,…,x^(n-2) (0)=η_n-2,x^(j)(T)=A,其中j∈I={0,1,2,…,n-1},得到了解的存在性和唯一性新的结果.     

Modified Mini finite element for the Stokes problem in ℝ2 or ℝ3

We analyze a modified version of the Mini finite element (or the Mini* finite element) for the Stokes problem in ℝ² or ℝ³. The cross‐grid element of order one in ℝ³ is also analyzed. The stability is verified with the aid of the macroelement technique introduced by Stenberg. Each of these methods converges with first order in h as the Mini element does. Numerical tests are given for the Mini* element in comparison with the Mini element when Ω is a unit square on ℝ². This revised version was published online in June 2006 with corrections to the Cover Date.     

Sample-path conservation laws,with applications to scheduling queues and fluid systems

The achievable-region approach, based on strong conservation laws, has most often been applied to stochastic scheduling and other control problems in the context of performance measures that are steady-state expected quantities. For some problems, however, strong conservation laws hold for performance measures at every time point on every sample path. We exploit this property to study optimal control for certain scheduling problems on a sample-path basis. Examples include preemptive scheduling to minimize a weighted sum of work in the system in each class, nonpreemptive scheduling to minimize a weighted sum of the number of customers in each class (when all classes have the same service-time distribution), and scheduling the processing of fluid in a multiclass fluid system operating in a random environment. The last problem is solved by considering the related Skorohod problem and its minimal solution. This revised version was published online in June 2006 with corrections to the Cover Date.     

Oscillations of higher order differential equations of neutral type

In this paper, sufficient conditions have been obtained for oscillation of solutions of a class of nth order linear neutral delay-differential equations. Some of these results have been used to study oscillatory behaviour of solutions of a class of boundary value problems for neutral hyperbolic partial differential equations.     

Recurrence relations for the coefficients of the Fourier series expansions with respect to q-classical orthogonal polynomials

We propose an algorithm to construct recurrence relations for the coefficients of the Fourier series expansions with respect to the q-classical orthogonal polynomials p_k(x;q). Examples dealing with inversion problems, connection between any two sequences of q-classical polynomials, linearization of ϑ_m(x) p_n(x;q), where ϑ_m(x) is x^mor (x;q)_m, and the expansion of the Hahn-Exton q-Bessel function in the little q-Jacobi polynomials are discussed in detail. This revised version was published online in June 2006 with corrections to the Cover Date.     

Numerical analysis of a quadratic matrix equation

The quadratic matrix equation AX²+ BX + C = 0in n x nmatricesarises in applications and is of intrinsic interest as oneof the simplest nonlinear matrix equations. We give a completecharacterization of solutions in terms of the generalized Schurdecomposition and describe and compare various numerical solutiontechniques. In particular, we give a thorough treatment offunctional iteration methods based on Bernoulli’s method.Other methods considered include Newton’s method with exact line searches, symbolic solution and continued fractions.We show that functional iteration applied to the quadraticmatrix equation can provide an efficient way to solve the associated quadratic eigenvalue problem (²A + B + C)x = 0.     

UNILATERAL EIGENVALUE PROBLEMS FOR NONLINEARLY ELASTIC PLATES： AN APPROACH VIA PSEUDO-MONOTONE OPERATORS

gi.TheTOpologicalDegreeforGeneralizedMonotoneOperatorsMonotoneoperatortheoryisoftenanefficienttoolforprovingtheexistenceofsolutionstononlinearProblems.Inparticular,thepseudo-monotoneoperatorsintroducedbyBrezis[2]areveryusefulforstudyingnonlinearellipticproblems.Weconsiderherethefollowingclassesofmappingsofgeneralizedmonotonetype.(QM)=theclassofquasi-mollotoneoperators,(S )=theclassofoperatorsoftype(S ),(PM)=theclassofpseudthmonotoneoperators,(LS)=theclassofLeray-Schauderoperators(compac…     

求线性规划对偶问题最优解的一种方法

线性规划对偶问题的最优解有重要的经济意义,中给出了一种较为简捷的求对偶问题最优解的方法。