Abstract. This paper presents a reformulation of Krylov Subspace Spectral (KSS) Methods, which build on Gene Golub’s many contributions pertaining to moments and Gaussian quadrature, to produce high-order accurate approximate solutions to variable-coefficient time-dependent PDE. This reformulation serves two useful purposes. First, it more clearly illustrates the distinction between KSS methods...

Non-linear image reconstruction methods are desirable for applications in electrical impedance tomography (EIT) such as brain or breast imaging where the assumptions of linearity are violated. We present a novel non-linear Newton-Krylov method for solving large-scale EIT inverse problems, which has the potential advantages of improved robustness and computational efficiency over previous method...

Krylov subspace methods are used for solving systems of linear equations Hx+ c = 0. We present a general Krylov subspace method that can be applied to a symmetric system of linear equations, i.e., for a system in which H = H . In each iteration, we have a choice of scaling of the orthogonal vectors that successively make the Krylov subspaces available. We define an extended representation of ea...

Numerical simulations of the behavior of machine tools are usually based on a finite element (FE) discretization of their mechanical structure. In order to capture all necessary details FE models are in general very large and sparse. Hence the computation of the simulation takes an unacceptable long time and requires much memory space. To calculate the results in reasonable time typically modal...

A High Performance Computing alternative to traditional Krylov subspace methods, pipelined Krylov subspace solvers offer better scalability in the strong scaling limit compared to standard Krylov subspace methods for large and sparse linear systems. The typical synchronization bottleneck is mitigated by overlapping time-consuming global communication phases with local computations in the algori...

The exponential time integration, i.e., time integrationwhich involves thematrix exponential, is an attractive tool for time domain modeling involving Maxwell’s equations. However, its application in practice often requires a substantial knowledge of numerical linear algebra algorithms, such as Krylov subspace methods. In this note we discuss exponential Krylov subspace time integrationmethods ...

We present low complexity, quickly converging robust adaptive beamformers that combine robust Capon beamformer (RCB) methods and data-adaptive Krylov subspace dimensionality reduction techniques. We extend a recently proposed reduced-dimension RCB framework, which ensures proper combination of RCBs with any form of dimensionality reduction that can be expressed using a full-rank dimension reduc...

We consider the approximation of the matrix φ-functions that appear in exponential integrators for stiff systems of differential equations. For stiff systems, the field-of-values of the occurring matrices is large and lies somewhere in the left complex half-plane. In order to obtain an efficient method uniformly for all matrices with a field-of-values in the left complex half-plane, we consider...

GMRES is a popular iterative method for the solution of large linear systems of equations with a square nonsymmetric matrix. The method generates a Krylov subspace in which an approximate solution is determined. We present modifications of the GMRES and the closely related RRGMRES methods that allow augmentation of the Krylov subspaces generated by these methods by a user-supplied subspace. We ...