The FEAST method for solving large sparse eigenproblems is equivalent to subspace iteration with an approximate spectral projector and implicit orthogonalization, in particular, when using rational approximants based on the work of Zolotarev.Expand

A novel parallel algorithm for the integration of linear initial-value problems is proposed based on the simple observation that homogeneous problems can typically be integrated much faster than inhomogeneous problems.Expand

Pade approximation is considered from the point of view of robust methods of numerical linear algebra, in particular, the singular value decomposition.Expand

Nonlinear eigenvalue problems arise in a variety of science and engineering applications and in the past ten years there have been numerous breakthroughs in the development of numerical methods.Expand

We utilize an integral representation for the error of the iterates in the Arnoldi method which allows us to develop an efficient quadrature-based restarting algorithm suitable for a large class of functions, including the so-called Stieltjes functions and the exponential function.Expand

A new construction of an absorbing boundary condition for indefinite Helmholtz problems on unbounded domains is presented, which converges exponentially fast in the number of grid points.Expand

Matrix functions are a central topic of linear algebra, and problems of their numerical approximation appear increasingly often in scientific computing. We review various rational Krylov methods for… Expand