Stabilizing Circulant Matrix in Modeling of Mechanical Structures Vibration using the Interior Point Methods

Circulant matrices that are positive semi-definite emerge in many engineering applications, where the data collected in a matrix do not maintain the specified structure. A special case application is the circulant matrices in mechanical structures vibration modeling. The goal is to recover initial matrix while preserving the physical structure. In this paper, after reformulating the problem into different formulas first as a semi-definite problem, then as a mixed semi-definite and second-order cone problem, subsequently, interior point method will be used to solve the problem. The results are compared with the interior point methods and the modified alternating projection method. Numerical results for the special circulant matrices generated from mechanical structures vibration modeling are presented.