The computational solution of problems can be restricted by the availability of solution
methods for linear (ized) systems of equations. In conjunction with iterative methods …

We briefly introduce typical and important direct and iterative methods for solving systems of
linear equations, concretely describe their fundamental characteristics in viewpoints of both …

This survey concerns subspace recycling methods, a popular class of iterative methods that
enable effective reuse of subspace information in order to speed up convergence and find …

GMRES is a popular Krylov subspace method for solving linear systems of equations
involving a general non-Hermitian coefficient matrix. The conventional bounds on GMRES …

This paper is about GMRES algorithms for the solution of nonsingular linear systems. We
first consider basic algorithms and study their convergence. We then focus on acceleration …

Learning neural operators for solving partial differential equations (PDEs) has attracted
great attention due to its high inference efficiency. However, training such operators requires …

Deflation is a well-known technique to accelerate Krylov subspace methods for solving
linear systems of equations. In contrast to preconditioning, in deflation methods singular …

In several applications, one needs to solve a sequence of linear systems with changing
matrices and right hand sides. This thesis concentrates on the analysis and application of …

Block GMRES is one of the most popular algorithms for solving large non-Hermitian linear
systems with multiple right-hand sides. The simpler block GMRES algorithm is a variation of …

The deflation technique for accelerating Krylov subspace iterative methods for the solution of
linear systems has long been well established. The first landmark papers of Nicolaides and …