Scalable Linear Solvers Based on Enlarged Krylov Subspaces with Dynamic Reduction of Search Directions

Acceleration of GPU-based Krylov solvers via data transfer reduction

Krylov subspace iterative solvers are often the method of choice when solving large sparse linear systems. At the same time, hardware accelerators such as graphics processing units continue to offer significant floating point performance gains for matrix and vector computations through easy-to-use libraries of computational kernels. However, as these libraries are usually composed of a well opt...

Interpolation-based Parametric Model Reduction using Krylov Subspaces

Iterative Methods Based on Krylov Subspaces

with a symmetric and positive definite operator A defined on a Hilbert space V with dimV = N and its preconditioned version PCG. We derive the CG from the projection in A-inner product point of view. We shall use (·, ·) for the standard inner product and (·, ·)A for the inner product introduced by the SPD operator A. When we say ‘orthogonal’ vectors, we refer to the default (·, ·) inner product...

Krylov space solvers for shifted linear systems

We investigate the application of Krylov space methods to the solution of shifted linear systems of the form (A+ σ)x− b = 0 for several values of σ simultaneously, using only as many matrix-vector operations as the solution of a single system requires. We find a suitable description of the problem, allowing us to understand known algorithms in a common framework and developing shifted methods b...

Krylov Subspaces Associated with Higher-order Linear Dynamical Systems

A standard approach to model reduction of large-scale higher-order linear dynamical systems is to rewrite the system as an equivalent first-order system and then employ Krylov-subspace techniques for model reduction of first-order systems. This paper presents some results about the structure of the block-Krylov subspaces induced by the matrices of such equivalent first-order formulations of hig...