Structured Quadratic Inverse Eigenvalue Problems From The Second-order RLC Circuit Designing

The QIEP(quadratic inverse eigenvalue problems) is a kind of mathematical problems that have close contact with the practical application,and almost all the problems have their own backgrounds,so the solving of such problems must take their unique backgrounds into account fully.In this paper,the development of QIEP,the relevant results from others and the problems I research now is introduced in the 1^st chapter,the necessary knowledge for researching QIEP are listed also in this chapter.In the 2^nd and 3^rd chapter,a kind of structured QIEP with practical application for designing the second-order LC circuit and RLC circuit is formulated.This kind of QIEP have special coefficient matrix structure,they are tridiagonal or diagonal,with the requirements of connectivity and positivity for the system also.For the second-order LC circuit designing,the problem is to reconstruct the coefficient matrices by only one pair of eigen information,and a simple algorithm that need to check the symbols three times is given.For the second-order RLC circuit designing,the problem is to reconstruct the coefficient matrices by two pair of eigen information.According to the structure of the coefficient matrices and the requirements of the physical parameters,the problem is transformed into a group of inequalities,which can be transformed into a minimax problem.Finally,the algorithms are programming by Matlab and experiments are given.