In this paper, a class of inverse problems of matrix equation AX=B is studied on the linear manifold, the necessary and sufficient conditions for the solvability of the inverse problem and the expression of the genera...In this paper, a class of inverse problems of matrix equation AX=B is studied on the linear manifold, the necessary and sufficient conditions for the solvability of the inverse problem and the expression of the general solution are given; at the same time, the best approximation problem is considered, the expression of the best approximate solution and the numerical method are also given. This paper extends the results in [1, 2].展开更多
In this article, a Ky Fan matching theorem for transfer compactly open covers is established. As applications, a Fan-Browder coincidence theorem, a Ky Fan best approximation theorem and a Brouwer-Schauder-Rothe type f...In this article, a Ky Fan matching theorem for transfer compactly open covers is established. As applications, a Fan-Browder coincidence theorem, a Ky Fan best approximation theorem and a Brouwer-Schauder-Rothe type fixed point theorem are obtained.展开更多
This paper, considers the following two problerns: Problem Ⅰ Given A ∈ Rm×n,B ∈ Rp×q,C ∈ Rm×q,G ∈ Rl×n,H ∈ Rp×t,D ∈ Rl×t find X ∈ Rn×p such that Problem Ⅱ Given A ∈ Rm×...This paper, considers the following two problerns: Problem Ⅰ Given A ∈ Rm×n,B ∈ Rp×q,C ∈ Rm×q,G ∈ Rl×n,H ∈ Rp×t,D ∈ Rl×t find X ∈ Rn×p such that Problem Ⅱ Given A ∈ Rm×n,C ∈E Rm×m,G ∈ Rl×n,D ∈ Rl×l,find X ∈ SRn×n such that. Where ‖·‖ is Frobenius norm, SRn×n = {X ∈ Rn×n: X = XT} By applying the generalized singular value decompositions (GSVD) of matrix pairs,we obtain the general form of the solutions of Problem Ⅰ and Problem Ⅱ.展开更多
The two classes of best approximation of a matrix on the linear manifold are discussed by using the row string operator and the generalized singular value decomposition of a matrix. The solutions of the problems and a...The two classes of best approximation of a matrix on the linear manifold are discussed by using the row string operator and the generalized singular value decomposition of a matrix. The solutions of the problems and a numerical method for solving the problems are given. The problems discussed in some papers could be subsumed in the cases proposed in this paper.展开更多
We discuss the best approximation of periodic functions by trigonometric polynomials and the approximation by Fourier partial summation operators, Valle-Poussin operators, Ces`aro operators, Abel opera-tors, and Jacks...We discuss the best approximation of periodic functions by trigonometric polynomials and the approximation by Fourier partial summation operators, Valle-Poussin operators, Ces`aro operators, Abel opera-tors, and Jackson operators, respectively, on the Sobolev space with a Gaussian measure and obtain the average error estimations. We show that, in the average case setting, the trigonometric polynomial subspaces are the asymptotically optimal subspaces in the L q space for 1≤q 【 ∞, and the Fourier partial summation operators and the Valle-Poussin operators are the asymptotically optimal linear operators and are as good as optimal nonlinear operators in the L q space for 1≤q 【 ∞.展开更多
Hudzik and Kurc discussed some best approximation problems in Banach lattices by means of monotonicities. This paper deals with more general best approximation problems in Banach lattices. Existence, uniqueness, stabi...Hudzik and Kurc discussed some best approximation problems in Banach lattices by means of monotonicities. This paper deals with more general best approximation problems in Banach lattices. Existence, uniqueness, stability and continuity for such best approximation problems are discussed.展开更多
In this paper, we find a way to give best simultaneous approximation of n arbitrary points in convex sets. First, we introduce a special hyperplane which is based on those n points. Then by using this hyperplane, we d...In this paper, we find a way to give best simultaneous approximation of n arbitrary points in convex sets. First, we introduce a special hyperplane which is based on those n points. Then by using this hyperplane, we define best approximation of each point and achieve our purpose.展开更多
文摘In this paper, a class of inverse problems of matrix equation AX=B is studied on the linear manifold, the necessary and sufficient conditions for the solvability of the inverse problem and the expression of the general solution are given; at the same time, the best approximation problem is considered, the expression of the best approximate solution and the numerical method are also given. This paper extends the results in [1, 2].
基金This work is supported by the Scientific Research Foundation of Bijie University.
文摘In this article, a Ky Fan matching theorem for transfer compactly open covers is established. As applications, a Fan-Browder coincidence theorem, a Ky Fan best approximation theorem and a Brouwer-Schauder-Rothe type fixed point theorem are obtained.
文摘This paper, considers the following two problerns: Problem Ⅰ Given A ∈ Rm×n,B ∈ Rp×q,C ∈ Rm×q,G ∈ Rl×n,H ∈ Rp×t,D ∈ Rl×t find X ∈ Rn×p such that Problem Ⅱ Given A ∈ Rm×n,C ∈E Rm×m,G ∈ Rl×n,D ∈ Rl×l,find X ∈ SRn×n such that. Where ‖·‖ is Frobenius norm, SRn×n = {X ∈ Rn×n: X = XT} By applying the generalized singular value decompositions (GSVD) of matrix pairs,we obtain the general form of the solutions of Problem Ⅰ and Problem Ⅱ.
文摘The two classes of best approximation of a matrix on the linear manifold are discussed by using the row string operator and the generalized singular value decomposition of a matrix. The solutions of the problems and a numerical method for solving the problems are given. The problems discussed in some papers could be subsumed in the cases proposed in this paper.
基金supported by National Natural Science Foundation of China(Grant No. 10871132)Beijing Natural Science Foundation (Grant No. 1102011)Key Programs of Beijing Municipal Education Commission (Grant No. KZ200810028013)
文摘We discuss the best approximation of periodic functions by trigonometric polynomials and the approximation by Fourier partial summation operators, Valle-Poussin operators, Ces`aro operators, Abel opera-tors, and Jackson operators, respectively, on the Sobolev space with a Gaussian measure and obtain the average error estimations. We show that, in the average case setting, the trigonometric polynomial subspaces are the asymptotically optimal subspaces in the L q space for 1≤q 【 ∞, and the Fourier partial summation operators and the Valle-Poussin operators are the asymptotically optimal linear operators and are as good as optimal nonlinear operators in the L q space for 1≤q 【 ∞.
基金Supported by National Natural Science Foundation of China, Grant (10471032)
文摘Hudzik and Kurc discussed some best approximation problems in Banach lattices by means of monotonicities. This paper deals with more general best approximation problems in Banach lattices. Existence, uniqueness, stability and continuity for such best approximation problems are discussed.
文摘In this paper, we find a way to give best simultaneous approximation of n arbitrary points in convex sets. First, we introduce a special hyperplane which is based on those n points. Then by using this hyperplane, we define best approximation of each point and achieve our purpose.
