An Alternating Projection Method For Model Updating Problems

The quadratic model updating problem has important applications in many fields of science and engineering. We mainly discuss the model updating problem with positive semi-definite coefficient matrices. The core idea of the paper comes from the alternating projection method that was first discovered by Von Neumann. In chapter1, we first give a brief introduction of the quadratic inverse eigenvalue problem, then describe the current development and the achieved results of the quadratic inverse eigenvalue problems. In chapter2, we introduce the model updating problem and the work we intend to do. In chapter3, we describe the history of the alternating projection method. In chapter4, we design the mathematical model and make the theoretical analysis, at last give the specific algorithm. In chapter5, with the help of the Matlab, we do lots of numerical experiments and demonstrate the effectiveness and robustness of this algorithm.