We consider three improvements to seed methods for Hermitian linear systems with multiple right-hand sides: only the Krylov subspace for the first system is used for seeding subsequent right-hand sides, the first right-hand side is solved past convergence, and periodic reorthogonalization is used in order to control roundoff errors associated with the Conjugate Gradient algorithm. The method is...

The repeated trapezoidal method was considered by P. Eggermont for the numerical solution of weakly singular Volterra integral equations of the first kind with exactly given right-hand sides ([7]). In the present paper we consider the regularizing properties of this method for perturbed right-hand sides. Finally, numerical results are presented.

In this paper, we propose a new seed projection method for solving shifted systems with multiple right-hand sides. This seed projection method uses a seed selection strategy. Numerical experiments are presented to show the efficiency of the newly method. Keywords—shifted systems, multiple right-hand sides, seed projection.

The large systems of complex linear equations that are generated in QCD problems often have multiple right-hand sides (for multiple sources) and multiple shifts (for multiple masses). Deflated GMRES methods have previously been developed for solving multiple right-hand sides. Eigenvectors are generated during solution of the first right-hand side and used to speed up convergence for the other r...