针对三维坐标转换模型中系数矩阵部分元素存在误差的问题,将观测向量和系数矩阵中的误差项组成新的改正数向量,重新构造拉格朗日方程。提出总体最小二乘(Total Least Square,TLS)迭代法求解三维坐标转换参数的新方法,只对系数矩阵中含...针对三维坐标转换模型中系数矩阵部分元素存在误差的问题,将观测向量和系数矩阵中的误差项组成新的改正数向量,重新构造拉格朗日方程。提出总体最小二乘(Total Least Square,TLS)迭代法求解三维坐标转换参数的新方法,只对系数矩阵中含误差的元素进行改正,同时保证系数矩阵中不同位置的相同元素具有相同改正数,理论模型更加严谨。最后,通过算例数据验证,结果表明新方法可行且解算结果更优。展开更多
This paper proposes a class of generalized mixed least square methods(GMLSM) forthe estimation of weights in the analytic hierarchy process and studies their good properties such asinvariance under transpose, invarian...This paper proposes a class of generalized mixed least square methods(GMLSM) forthe estimation of weights in the analytic hierarchy process and studies their good properties such asinvariance under transpose, invariance under change of scale, and also gives a simple convergent iterativealgorithm and some numerical examples. The well-known eigenvector method(EM) is then compared.Theoretical analysis and the numerical results show that the iterative times of the GMLSM are generallyfewer than that of the MLSM, and the GMLSM are preferable to the EM in several important respects.展开更多
Based on the concept of multiplicative fuzzy consistent complementary judgement matrix, the mixed least square method （MLSM） for priority of complementary judgement matrix is proposed and proved. Then, the correspon...Based on the concept of multiplicative fuzzy consistent complementary judgement matrix, the mixed least square method （MLSM） for priority of complementary judgement matrix is proposed and proved. Then, the corresponding convergent iterative algorithm is given and its convergence is proved. Finally, some main properties of the developed priority method, such as rank preservation under strong condition, etc., ate introduced. The theoretical analyses show that the MLSM can sufficiently reflect the preference information of the decision maker, and is easy to realize on a computer.展开更多
The mathematical model for two-phase displacement in porous media is a coupled initial boundary value problem of nonlinear partial differential equations which consist of a pressure equation and a saturation equation....The mathematical model for two-phase displacement in porous media is a coupled initial boundary value problem of nonlinear partial differential equations which consist of a pressure equation and a saturation equation. In this paper, the mixed least-square weak form of pressure equation is got, and the positive definite characteristics of the weak form is proved. Based on this weak form, a new kind of numerical methods for two-phase displacement problems is proposed: the mixed least-square finite element method is used to solve pressure and Darcy velocity, and the saturation is solved by using characteristic finite element method. The main merits of the mixed least-square finite element method compared with mixed finite element method are: first, the structure of the mixed least-square finite el- ement spaces is just standard finite element spaces, it is simple and easy to use; second, the weak form of the mixed least-square finite element method for pressure is symetric and definite positive, thus there are many efficient methods to solve numerically; and the last, the Darcy velocity solved by mixed least-square finite element method is continuous. In numerical analyses, a very important inequality is obtained which is used to control the errors of the pressure and Darcy velocity, and the optimal error estomates of the proposed method are proved.展开更多
文摘针对三维坐标转换模型中系数矩阵部分元素存在误差的问题,将观测向量和系数矩阵中的误差项组成新的改正数向量,重新构造拉格朗日方程。提出总体最小二乘(Total Least Square,TLS)迭代法求解三维坐标转换参数的新方法,只对系数矩阵中含误差的元素进行改正,同时保证系数矩阵中不同位置的相同元素具有相同改正数,理论模型更加严谨。最后,通过算例数据验证,结果表明新方法可行且解算结果更优。
文摘This paper proposes a class of generalized mixed least square methods(GMLSM) forthe estimation of weights in the analytic hierarchy process and studies their good properties such asinvariance under transpose, invariance under change of scale, and also gives a simple convergent iterativealgorithm and some numerical examples. The well-known eigenvector method(EM) is then compared.Theoretical analysis and the numerical results show that the iterative times of the GMLSM are generallyfewer than that of the MLSM, and the GMLSM are preferable to the EM in several important respects.
基金The Project of Shaanxi Provincial Natural Science Foundation of China (No.2004A05)the Project of Science and Research Foundation of Education Committee of Shaanxi Province (No.06JK324)
文摘Based on the concept of multiplicative fuzzy consistent complementary judgement matrix, the mixed least square method （MLSM） for priority of complementary judgement matrix is proposed and proved. Then, the corresponding convergent iterative algorithm is given and its convergence is proved. Finally, some main properties of the developed priority method, such as rank preservation under strong condition, etc., ate introduced. The theoretical analyses show that the MLSM can sufficiently reflect the preference information of the decision maker, and is easy to realize on a computer.
文摘The mathematical model for two-phase displacement in porous media is a coupled initial boundary value problem of nonlinear partial differential equations which consist of a pressure equation and a saturation equation. In this paper, the mixed least-square weak form of pressure equation is got, and the positive definite characteristics of the weak form is proved. Based on this weak form, a new kind of numerical methods for two-phase displacement problems is proposed: the mixed least-square finite element method is used to solve pressure and Darcy velocity, and the saturation is solved by using characteristic finite element method. The main merits of the mixed least-square finite element method compared with mixed finite element method are: first, the structure of the mixed least-square finite el- ement spaces is just standard finite element spaces, it is simple and easy to use; second, the weak form of the mixed least-square finite element method for pressure is symetric and definite positive, thus there are many efficient methods to solve numerically; and the last, the Darcy velocity solved by mixed least-square finite element method is continuous. In numerical analyses, a very important inequality is obtained which is used to control the errors of the pressure and Darcy velocity, and the optimal error estomates of the proposed method are proved.
