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Abstract: In this paper, we present an efficient numerical algorithm to find exact solutions for the system of linear equations based on homotopy perturbation method (HPM). A reliable modification is proposed, and the modified method is employed to solve the system of linear equations; the results are compared with those obtained by the original homotopy perturbation method. Two examples are given to illustrate the ability and reliability of the modified method. The results reveal that the modified method is very simple and effective. [Copyright &y& Elsevier]

Based on the identification technique of active constraints, we propose a Newton-like algorithm and a quasi-Newton algorithm for solving the box-constrained optimization problem. The two algorithms require only the solution of a lower-dimensional system of linear equations at each iteration. In the proposed quasi-Newton algorithm, we make use of an approximate direction derivative of the multiplier functions so that only first-order derivatives of the objective function are needed to evaluate. Under mild assumptions, global convergence of the two algorithms is established. In particular, locally quadratic convergence for the Newton-like algorithm and locally superlinear convergence for the quasi-Newton algorithm are obtained without assuming that the strict complementarity condition holds at the solution. [Copyright &y& Elsevier]