Generalized inverse problems for part symmetric matrices on a subspace in structural dynamic model updating

Authors:
Xian-Xia Liu;Jiao-Fen Li;Xi-Yan Hu
Affiliations:
College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, People's Republic of China;School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, People's Republic of China and College of Mathematics and Econometrics, Hunan University ...;College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, People's Republic of China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2011

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Abstract

An nxn matrix A is said to be M-symmetric if x^T(A-A^T)=0 for all x@?R(M), where M@?R^n^x^p is given. In this paper, by extending the idea of the conjugate gradient least squares (CGLS) method, we construct an iterative method for solving a generalized inverse eigenvalue problem: minimizing @?X^TAX-C@? where @?@?@? is the Frobenius norm, X@?R^n^x^m and C@?R^m^x^m are given, and A@?R^n^x^n is a M-symmetric matrix to be solved. Our algorithm produces a suitable A such that X^TAX=C within finite iteration steps in the absence of roundoff errors, if such an A exists. We show that the algorithm is stable any case, and we give results of numerical experiments that support this claim.