A Stochastic Estimation of Eigenvalue Counts in an Interval


16:00:00 - 18:00:00

R430 , Astronomy and Mathematics Building

Based on Sylvester’s law of inertia, LDL^T decomposition can be used to compute the number of eigenvalues of a Hermitian matrix within a given interval. This approach can lead to highly accurate eigenvalue counts with a high cost. Another approach is iterative stochastic type scheme, which mainly relies on matrix-vector multiplications. The method is cheaper especially for sparse matrices and can be adaptively stopped with a satisfactory estimation of eigenvalue counts. We will introduce such stochastic approach based on the polynomial expansion filtering and discuss an implementation of the scheme in MATLAB and C language.