The problem of correcting simultaneously mass and stiffness matrices of finite element model of undamped structural systems using vibration tests is considered in this paper.The desired matrix properties,including sat...The problem of correcting simultaneously mass and stiffness matrices of finite element model of undamped structural systems using vibration tests is considered in this paper.The desired matrix properties,including satisfaction of the characteristic equation,symmetry,positive semidefiniteness and sparsity,are imposed as side constraints to form the optimal matrix pencil approximation problem.Using partial Lagrangian multipliers,we transform the nonlinearly constrained optimization problem into an equivalent matrix linear variational inequality,develop a proximal point-like method for solving the matrix linear variational inequality,and analyze its global convergence.Numerical results are included to illustrate the performance and application of the proposed method.展开更多
This paper generalizes the basic principle of multiplier-enlargement approach to approximating any nonbounded continuous functions with positive linear operators, and as an example, Bernstein polynomial operators are ...This paper generalizes the basic principle of multiplier-enlargement approach to approximating any nonbounded continuous functions with positive linear operators, and as an example, Bernstein polynomial operators are analysed and studied. This paper gives a certain theorem as a general rule to approximate any nonbounded continuous functions.展开更多
There have been many elegant results discussing the approximation proper- ties of the Bieberbach polynomials. However, very few papers investigated the approxi- mation properties of the extremal polynomials over Jorda...There have been many elegant results discussing the approximation proper- ties of the Bieberbach polynomials. However, very few papers investigated the approxi- mation properties of the extremal polynomials over Jordan curves. In the present paper, some results on a class of extremal polynomials over C1+αsmooth Jordan curves are obtained.展开更多
基金The work was supported by the National Natural Science Foundation of China(No.11571171)。
文摘The problem of correcting simultaneously mass and stiffness matrices of finite element model of undamped structural systems using vibration tests is considered in this paper.The desired matrix properties,including satisfaction of the characteristic equation,symmetry,positive semidefiniteness and sparsity,are imposed as side constraints to form the optimal matrix pencil approximation problem.Using partial Lagrangian multipliers,we transform the nonlinearly constrained optimization problem into an equivalent matrix linear variational inequality,develop a proximal point-like method for solving the matrix linear variational inequality,and analyze its global convergence.Numerical results are included to illustrate the performance and application of the proposed method.
文摘This paper generalizes the basic principle of multiplier-enlargement approach to approximating any nonbounded continuous functions with positive linear operators, and as an example, Bernstein polynomial operators are analysed and studied. This paper gives a certain theorem as a general rule to approximate any nonbounded continuous functions.
基金Supported by the National Science Foundation of China (19771006)
文摘There have been many elegant results discussing the approximation proper- ties of the Bieberbach polynomials. However, very few papers investigated the approxi- mation properties of the extremal polynomials over Jordan curves. In the present paper, some results on a class of extremal polynomials over C1+αsmooth Jordan curves are obtained.
