Spectral analysis of large sparse matrices for scalable direct solvers

Abstract

It is significant to perform structural analysis of large sparse matrices in order to obtain scalable direct solvers. In this paper, we focus on spectral analysis of large sparse matrices. We believe that the approach for exception handling of challenging matrices via Gerschgorin circles and using tuned parameters is beneficial and practical to stabilize the performance of sparse direct solvers. Nearly defective matrices are among challenging matrices for the performance of solver. Such matrices should be handled separately in order to get rid of potential performance bottleneck. Clustered eigenvalues observed via Gerschgorin circles may be used to detect nearly defective matrix. We observe that the usage of super-nodal storage parameters affects the number of fill-ins and memory usage accordingly.