一类带子块约束的特征值反问题  

An inverse eigenvalue problem with the submatrix constraint

作　　者：徐娇 XU Jiao(College of Mathematics and Statistics,Hubei Normal University,Huangshi 435002,China)

机构地区：[1]湖北师范大学数学与统计学院,湖北黄石435002

出　　处：《湖北师范大学学报（自然科学版）》2020年第1期24-31,共8页Journal of Hubei Normal University：Natural Science

摘　　要：有限元模型误差主要来自结构的几何形状、边界条件和受力状态等情况复杂部位,也即结构动力学模型的物理参数矩阵中仅部分元素存在明显误差,因而有限元模型修正问题可归结为带子块约束的特征值反问题(SC-IEP)与最佳逼近问题(OAP).通过矩阵对的广义奇异值分解,得到了问题SC-IEP的通解表示;证明了问题OAP的解存在唯一,并给出了在Frobenius范数意义下,最逼近有限元刚度矩阵的最佳修正刚度矩阵的显式表示。The finite element model errors mainly come from the complex parts of the geometry,boundary conditions and stress state of the structure,and some of the elements in the physical parameter matrices of the structural dynamics model have obvious errors,so the finite element model correction problems are the inverse eigenvalue problem with submatrix constraint(SC-IEP)and the optimal approximation problem(OAP).In this paper,the representation of the general solution of the inverse eigenvalue problem is obtained by applying the generalized singular value decomposition of a matrix pair.It is proved that the solution of the problem OAP exists uniquely.The given explicit representation of the best modified stiffness matrix closest to the finite element stiffness matrix in the Frobenius norm sense.

关 键 词：反问题 子块约束 广义奇异值分解 最佳逼近问题 

分 类 号：O241.6[理学—计算数学]