It is well-known that Bernstein polynomials are very important in studying the characters of smoothness in theory of approximation. A new type of combinations of Bernstein operators are given in [1]. In this paper, we...It is well-known that Bernstein polynomials are very important in studying the characters of smoothness in theory of approximation. A new type of combinations of Bernstein operators are given in [1]. In this paper, we give the Bernstein-Markov inequalities with step-weight functions for combinations of Bernstein polynomials with inner singularities as well as direct and inverse theorems.展开更多
In the teaching and researching of linear regression analysis, it is interesting and enlightening to explore how the dependent variable vector can be inner-transformed into regression coefficient estimator vector from...In the teaching and researching of linear regression analysis, it is interesting and enlightening to explore how the dependent variable vector can be inner-transformed into regression coefficient estimator vector from a visible geometrical view. As an example, the roadmap of such inner transformation is presented based on a simple multiple linear regression model in this work. By applying the matrix algorithms like singular value decomposition (SVD) and Moore-Penrose generalized matrix inverse, the dependent variable vector lands into the right space of the independent variable matrix and is metamorphosed into regression coefficient estimator vector through the three-step of inner transformation. This work explores the geometrical relationship between the dependent variable vector and regression coefficient estimator vector as well as presents a new approach for vector rotating.展开更多
The definition of block independence in generalized inverse of block matrix was introduced in [1]. In this paper, we give some equivalent conditions for two m × n matrices being block independent in reflexive inn...The definition of block independence in generalized inverse of block matrix was introduced in [1]. In this paper, we give some equivalent conditions for two m × n matrices being block independent in reflexive inner inverse .展开更多
By applying the multiple quotient singular value decomposition QQQQQ-SVD, we study the block independence in g-inverse and reflexive inner inverse of 2× 2 partitioned matrices, and prove a conjecture in [Yiju Wan...By applying the multiple quotient singular value decomposition QQQQQ-SVD, we study the block independence in g-inverse and reflexive inner inverse of 2× 2 partitioned matrices, and prove a conjecture in [Yiju Wang, SIAM J. Matrix Anal. Appl., 19（2）, 407-415（1998）].展开更多
In this paper, we investigate the perturbation problem for the Moore-Penrose bounded quasi-linear projection generalized inverses of a closed linear operaters in Banach space. By the method of the perturbation analysi...In this paper, we investigate the perturbation problem for the Moore-Penrose bounded quasi-linear projection generalized inverses of a closed linear operaters in Banach space. By the method of the perturbation analysis of bounded quasi-linear operators, we obtain an explicit perturbation theorem and error estimates for the Moore-Penrose bounded quasi-linear generalized inverse of closed linear operator under the T-bounded perturbation, which not only extend some known results on the perturbation of the oblique projection generalized inverse of closed linear operators, but also extend some known results on the perturbation of the Moore-Penrose metric generalized inverse of bounded linear operators in Banach spaces.展开更多
This study addresses the parameter identification problem in a system of time-dependent quasi-linear partial differential equations(PDEs).Using the integral equation method,we prove the uniqueness of the inverse probl...This study addresses the parameter identification problem in a system of time-dependent quasi-linear partial differential equations(PDEs).Using the integral equation method,we prove the uniqueness of the inverse problem in nonlinear PDEs.Moreover,using the method of successive approximations,we develop a novel iterative algorithm to estimate sorption isotherms.The stability results of the algorithm are proven under both a priori and a posteriori stopping rules.A numerical example is given to show the efficiency and robustness of the proposed new approach.展开更多
文摘It is well-known that Bernstein polynomials are very important in studying the characters of smoothness in theory of approximation. A new type of combinations of Bernstein operators are given in [1]. In this paper, we give the Bernstein-Markov inequalities with step-weight functions for combinations of Bernstein polynomials with inner singularities as well as direct and inverse theorems.
文摘In the teaching and researching of linear regression analysis, it is interesting and enlightening to explore how the dependent variable vector can be inner-transformed into regression coefficient estimator vector from a visible geometrical view. As an example, the roadmap of such inner transformation is presented based on a simple multiple linear regression model in this work. By applying the matrix algorithms like singular value decomposition (SVD) and Moore-Penrose generalized matrix inverse, the dependent variable vector lands into the right space of the independent variable matrix and is metamorphosed into regression coefficient estimator vector through the three-step of inner transformation. This work explores the geometrical relationship between the dependent variable vector and regression coefficient estimator vector as well as presents a new approach for vector rotating.
基金Supported by NNSF of China(10171055)and NSF of Shandong Province(Q99A11)
文摘The definition of block independence in generalized inverse of block matrix was introduced in [1]. In this paper, we give some equivalent conditions for two m × n matrices being block independent in reflexive inner inverse .
基金the National Natural Science Foundation of China,Grant No.10371044
文摘By applying the multiple quotient singular value decomposition QQQQQ-SVD, we study the block independence in g-inverse and reflexive inner inverse of 2× 2 partitioned matrices, and prove a conjecture in [Yiju Wang, SIAM J. Matrix Anal. Appl., 19（2）, 407-415（1998）].
基金Supported by National Nature Science Foundation of China(Grant No.11471091)
文摘In this paper, we investigate the perturbation problem for the Moore-Penrose bounded quasi-linear projection generalized inverses of a closed linear operaters in Banach space. By the method of the perturbation analysis of bounded quasi-linear operators, we obtain an explicit perturbation theorem and error estimates for the Moore-Penrose bounded quasi-linear generalized inverse of closed linear operator under the T-bounded perturbation, which not only extend some known results on the perturbation of the oblique projection generalized inverse of closed linear operators, but also extend some known results on the perturbation of the Moore-Penrose metric generalized inverse of bounded linear operators in Banach spaces.
基金supported by the National Natural Science Foundation of China(No.12171036)Beijing Natural Science Foundation(No.Z210001)the NSF of China No.11971221,Guangdong NSF Major Fund No.2021ZDZX1001,the Shenzhen Sci-Tech Fund Nos.RCJC20200714114556020,JCYJ20200109115422828 and JCYJ20190809150413261,National Center for Applied Mathematics Shenzhen,and SUSTech International Center for Mathematics.
文摘This study addresses the parameter identification problem in a system of time-dependent quasi-linear partial differential equations(PDEs).Using the integral equation method,we prove the uniqueness of the inverse problem in nonlinear PDEs.Moreover,using the method of successive approximations,we develop a novel iterative algorithm to estimate sorption isotherms.The stability results of the algorithm are proven under both a priori and a posteriori stopping rules.A numerical example is given to show the efficiency and robustness of the proposed new approach.
