Many advances in the development of Krylov subspace methods for the iterative solution of
linear systems during the last decade and a half are reviewed. These new developments …

We survey the quadratic eigenvalue problem, treating its many applications, its
mathematical properties, and a variety of numerical solution techniques. Emphasis is given …

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 …

We consider linear systems A(α)x(α)=b(α) depending on possibly many parameters
α=(\alpha_1,...,\alpha_p). Solving these systems simultaneously for a standard discretization …

Complex valued systems of equations with a matrix R+ 1S where R and S are real valued
arise in many applications. A preconditioned iterative solution method is presented when R …

The paper deals with the numerical treatment of the direct frequency domain (DFD) analysis
of linear mechanical systems. Attention is mainly focused on the solution of the complex …

Matrix square roots and their inverses arise frequently in machine learning, eg, when
sampling from high-dimensional Gaussians N (0, K) or “whitening” a vector b against …

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 …

We present a unified and self-contained treatment of rational Krylov methods for
approximating the product of a function of a linear operator with a vector. With the help of …

Tikhonov--Phillips regularization is one of the best-known regularization methods for inverse
problems. A posteriori criteria for determining the regularization parameter α require solving …