Algebraic correction methods for two-dimensional eigenvalue problems

Abstract

Eigenvalue problems, in their many forms, play an important role in many branches of applied mathematics. One of the reasons for this is that eigenvalue problems model vibrating systems, with the eigenvalue determining the frequencies of vibration. The natural approach to the eigenvalue problem is to calculate the eigenvalues from a knowledge of the underlying system. This is known as the forward problem. In many important applications in physics and medicine, the details of the underlying system are unknown, but the vibrations produced by the system can be measured. The problem is to determine information about the underlying system from the vibrations it produces. In terms of the eigenvalue problem, this is equivalent to reconstructing the underlying system from the eigenvalues. This is known as the inverse problem.