Gersgorin Disks, a Maple Program Example

Olga became instrumental to the field of matrix theory. During WW II, she was working at the National Physical Laboratory in London, doing research with the flutter group. Flutter is a phenomena in flight that is related to the interaction of the elastic forces in the airframe of an aircraft and the aerodynamic forces being exerted on the aircraft. She found a way to simplify the process by first looking for the eigenvalues using the Gersgorin theorem. Each eigenvalue can be found within the parameters of a Gersgorin disk. The following program on maple is an example of this process. During the program animation, as the eigenvalue changes, so does the location of the Gersgorin disk. Olga’s matrices were much more difficult than the examples provided in the computer program. The eigenvalues of her equations were too time consuming to calculate, so her graph would have told her where to look for the eigenvalues, and reduced the amount of calculations considerably. She also did further analysis, beyond the scope of this paper, that made the disks smaller. The example given here would have only been the beginning stages of finding the flutter parameter. (This example was made possible by Dr. Bill Bauldry’s program, found at ).