A Method for Profiling the Distribution of Eigenvalues Using the as Method

This paper is concerned with solving large-scale eigenvalue problems by algebraic sub-structuring and contour integral. We combine Algebraic Sub-structuring (AS) method and the Contour Integral Rayleigh-Ritz (CIRR) method. The AS method calculates approximate eigenpairs fast and has been shown to be efficient for vibration and acoustic analysis. However, the application areas of this method have been limited because its accuracy is usually lower than other methods. On the other hand, if the appropriate domains are chosen, the CIRR method produces accurate solutions. However, it is difficult to choose these domains without the information of eigenvalue distribution. We propose a combination of AS and CIRR such as the AS method is used as a method for profiling a distribution of eigenvalues, and the accurate solutions are produced by the CIRR method using the information of eigenvalue distribution provided by AS. We show our method is effective from the result of applying this method to the molecular orbital calculations.