Search

Abstract: In this paper, we develop dwindling filter idea and trust region strategy for solving nonlinear optimization. Compared with traditional filter trust region algorithm, the new filter algorithm has more flexibility for the acceptance of the trial step and the feasibility restoration phase is not needed. Under mild conditions, the global convergence of the new algorithm is analyzed. Preliminary numerical results are reported. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a dwindling filter inexact projected Hessian algorithm for solving large scale nonlinear constrained optimization. For large-scale applications, inexact projected Hessian algorithm is needed to get search direction by solving one or more linear systems approximately using iterative linear algebra techniques. The envelope of the dwindling filter becomes thinner and thinner as the step size approaches zero so that the new filter has more flexibility for the acceptance of the trial step compared with traditional filter. Under mild conditions, global convergence and local superlinear convergence rate are obtained. The numerical experiments are reported to show the effectiveness of the proposed algorithm for large scale problems. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a filter algorithm for nonlinear systems of equalities and inequalities. In the algorithm, the systems of nonlinear equalities and inequalities are transformed into a nonlinear programming problem. The new algorithm uses the non-monotone technique in conjunction with filter idea and a global line search strategy that ensures convergence from any starting point. Under mild conditions, global convergence and local superlinear convergence rate are obtained. Numerical results demonstrate that the new algorithm is effective. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a nonmonotone filter Diagonalized Quasi-Newton Multiplier (DQMM) method for solving system of nonlinear equations. The system of nonlinear equations is transformed into a constrained nonlinear programming problem which is then solved by nonmonotone filter DQMM method. A nonmonotone criterion is used to speed up the convergence progress in some ill-conditioned cases. Under reasonable conditions, we give the global convergence properties. The numerical experiments are reported to show the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: A Cramer rule for solving a kind of restricted matrix equationsis presented in [G. Wang, Jie Sun, A Cramer rule for solution of the general restricted matrix equation, Appl. Math. Comput. 154 (2004) 415–422]. This paper gives a more condensed Cramer rule for the solution of the matrix equations. The results in [G. Wang, Z.L. Xu, Solving a kind of restricted matrix equations and Cramer rule, Appl. Math. Comput. 162 (2005) 329–338, Chao Gu, G.R. Wang, Z.L. Xu, PCR Algorithm for the Parallel Computation of the Solution of a class of Singular linear Systems, Appl. Math. Comput. 176 (2006) 237–244] are partially the special cases in our paper. [Copyright &y& Elsevier]

Abstract: The paper presents a new highly parallel algorithm for computing the solution of a class of singular linear systemsBy the algorithm the solution x = A d,W b is obtained in steps with P = mn processors when n ⩾2(m −1) and with P =2m(m −1) processors otherwise. [Copyright &y& Elsevier]

In this paper, we introduce a PQ-norm and discuss the condition number of the W-weighted Drazin inverse. We get some results on the condition number with respect to Ad,w and singular linear systems WAWx=b,b∈R((WA)k2), x∈R((AW)k1) which are similar to the regular inverse A-1 and nonsingular linear systems Ax=b. [Copyright &y& Elsevier]

Abstract: By using the method of generalized singular values decomposition, we establish a canonical theorem for a pair of oblique projectors and , give some new results for perturbations of and , where is the weighted Moore–Penrose inverse of matrix A, M and N are two Hermitian positive definite matrices and B is a matrix obtained from a perturbation of A. Our work can be seen as the extended results for orthogonal projectors and . Some numerical examples are given to illustrate the results. [Copyright &y& Elsevier]

Abstract: The method of designing electromagnetic invisible cloak is usually based on the form-invariance of Maxwell’s equations in coordinate transformation. By solving the partial differential equations (PDEs) that describe how the coordinates transform, three-dimensional (3-D) electromagnetic and acoustic invisible cloaks with arbitrary shapes can be designed provided the boundary conditions of the cloaks can be determined by the corresponding transformation. Full wave simulations based on finite element method verify the designed cloaks. The proposed method can be easily used in designing other transformation media such as matter-wave cloaks. [Copyright &y& Elsevier]