This paper is mainly concerned with solving the following two problems: Problem Ⅰ. Given X ∈ Rn×m, B . Rm×m. Find A ∈ Pn such thatwhereProblem Ⅱ. Given A ∈Rn×n. Find A ∈ SE such thatwhere F is Fro...This paper is mainly concerned with solving the following two problems: Problem Ⅰ. Given X ∈ Rn×m, B . Rm×m. Find A ∈ Pn such thatwhereProblem Ⅱ. Given A ∈Rn×n. Find A ∈ SE such thatwhere F is Frobenius norm, and SE denotes the solution set of Problem I.The general solution of Problem I has been given. It is proved that there exists a unique solution for Problem II. The expression of this solution for corresponding Problem II for some special case will be derived.展开更多
This paper presents a trust region algorithm for nonlinear problems of equalities and inequalities. The problem is changed to a least-squares problem with non-negative constraints by using slack variables. An equivale...This paper presents a trust region algorithm for nonlinear problems of equalities and inequalities. The problem is changed to a least-squares problem with non-negative constraints by using slack variables. An equivalent KKT condition is derived, which is the base of constracting the new algorithm. The global conver- gence is established under general conditions, and a local quadratic convergence is proved for nondegenerate point satisfying second-order sufficient conditions. Numerical tests for our algorithm are also presented.展开更多
The practical method is proposed in this papers which is based on the iterative method for solving linear system of equations. The normal equations are solved directly by the algorithm and a minimum norm solution can ...The practical method is proposed in this papers which is based on the iterative method for solving linear system of equations. The normal equations are solved directly by the algorithm and a minimum norm solution can be obtained when coefficient matrix of normal equation is singular, so that the sequence generated by the algorithm may be convergent. The numerical examples illustrate the algorithm is very efficient for singular problem or ill-condition problem.展开更多
基金Supported by the National Nature Science Fundation of China.
文摘This paper is mainly concerned with solving the following two problems: Problem Ⅰ. Given X ∈ Rn×m, B . Rm×m. Find A ∈ Pn such thatwhereProblem Ⅱ. Given A ∈Rn×n. Find A ∈ SE such thatwhere F is Frobenius norm, and SE denotes the solution set of Problem I.The general solution of Problem I has been given. It is proved that there exists a unique solution for Problem II. The expression of this solution for corresponding Problem II for some special case will be derived.
文摘This paper presents a trust region algorithm for nonlinear problems of equalities and inequalities. The problem is changed to a least-squares problem with non-negative constraints by using slack variables. An equivalent KKT condition is derived, which is the base of constracting the new algorithm. The global conver- gence is established under general conditions, and a local quadratic convergence is proved for nondegenerate point satisfying second-order sufficient conditions. Numerical tests for our algorithm are also presented.
文摘The practical method is proposed in this papers which is based on the iterative method for solving linear system of equations. The normal equations are solved directly by the algorithm and a minimum norm solution can be obtained when coefficient matrix of normal equation is singular, so that the sequence generated by the algorithm may be convergent. The numerical examples illustrate the algorithm is very efficient for singular problem or ill-condition problem.
