Abstract
Shifted linear systems arise in many important applications such as lattice quantum chromodynamics, large-scale electronic structure theory, and quadratic optimization problems. Recent strong need for solving the extremely large shifted linear systems enhance the importance of designing efficient solvers. As a candidate to satisfy the need, iterative methods using Krylov subspaces and the shift-invariance property have been attracting much interest. The primary aim of this paper is to survey the successful iterative methods and to classify them in terms of Krylov subspace methods.
