This paper discusses the solutions of the linear matrix equation BT X B=Don some linear manifolds.Some necessary and sufficient conditions for the existenceof the solution and the expression of the general solution ar...This paper discusses the solutions of the linear matrix equation BT X B=Don some linear manifolds.Some necessary and sufficient conditions for the existenceof the solution and the expression of the general solution are given.And also someoptimal approximation solutions are discussed.展开更多
A class of regularized conjugate gradient methods is presented for solving the large sparse system of linear equations of which the coefficient matrix is an ill-conditioned symmetric positive definite matrix. The conv...A class of regularized conjugate gradient methods is presented for solving the large sparse system of linear equations of which the coefficient matrix is an ill-conditioned symmetric positive definite matrix. The convergence properties of these methods are discussed in depth, and the best possible choices of the parameters involved in the new methods are investigated in detail. Numerical computations show that the new methods are more efficient and robust than both classical relaxation methods and classical conjugate direction methods.展开更多
We establish the convergence theories of the symmetric relaxation methods for the system of linear equations with symmetric positive definite coefficient matrix, and more generally, those of the unsymmetric relaxation...We establish the convergence theories of the symmetric relaxation methods for the system of linear equations with symmetric positive definite coefficient matrix, and more generally, those of the unsymmetric relaxation methods for the system of linear equations with positive definite matrix.展开更多
基金This work was supposed by the National Nature Science Foundation of China
文摘This paper discusses the solutions of the linear matrix equation BT X B=Don some linear manifolds.Some necessary and sufficient conditions for the existenceof the solution and the expression of the general solution are given.And also someoptimal approximation solutions are discussed.
基金Subsidized by The Special Funds For Major State Basic Research Projects G1999032803.
文摘A class of regularized conjugate gradient methods is presented for solving the large sparse system of linear equations of which the coefficient matrix is an ill-conditioned symmetric positive definite matrix. The convergence properties of these methods are discussed in depth, and the best possible choices of the parameters involved in the new methods are investigated in detail. Numerical computations show that the new methods are more efficient and robust than both classical relaxation methods and classical conjugate direction methods.
文摘We establish the convergence theories of the symmetric relaxation methods for the system of linear equations with symmetric positive definite coefficient matrix, and more generally, those of the unsymmetric relaxation methods for the system of linear equations with positive definite matrix.
