Acoustic eigenvalue estimation using Rayleigh quotient iteration with a sparse matrix pencil

Abstract

Various methods for estimating acoustic eigenvalues from a measured signal can be found in the literature. Among these methods, the matrix pencil method is a popular choice. The matrix pencil method provides reasonable eigenvalue estimates, albeit alongside several spurious estimates. This work uses Rayleigh quotient iteration to avoid these spurious values. Additionally, a sparse matrix structure is used to write the matrix pencil. The approach is verified using simulated data and validated using measured data. When reliable initial guesses for a few eigenvalues are available, the proposed method provides efficient and accurate eigenvalue estimates.