Efficient subspace iteration with Chebyshev-type filtering

Abstract

Shift-invert and other methods for computing inner eigenvalues often require the solution of linear systems. This may become a problem if the linear systems are very ill-conditioned and the matrix dimension precludes the use of direct solvers. Then eigensolvers with polynomial acceleration become particularly attractive because they avoid the solution of linear systems. We discuss techniques for increasing the efficiency of subspace iteration with polynomial filtering. These include reducing the polynomial degree by adapting Chebyshev-based filter functions, optimizing the size of the search space, and using tailored high-performance computational kernels.