58 citations · 100 across the 13 of their papers we have counts for
16 papers
Do you precondition on the left or on the right?
Nicole Spillane, Pierre Matalon, Daniel B Szyld
This work is a follow-up to a poster that was presented at the DD29 conference. Participants were asked the question: ``Do you precondition on the left or on the right?''. Here we…
Multiprecision computations with Schwarz methods
Michal Outrata, Daniel B. Szyld
Schwarz methods and preconditioners, where the approximate solution of the local problems is performed at a lower precision, i.e., with fewer digits of accuracy than in the underly…
Improved Polynomial Bounds and Acceleration of GMRES by Solving a min-max Problem on Rectangles, and by Deflating
Nicole Spillane, Daniel B Szyld
Polynomial convergence bounds are considered for left, right, and split preconditioned GMRES. They include the cases of Weighted and Deflated GMRES for a linear system Ax = b. In p…
New Convergence Analysis of GMRES with Weighted Norms, Preconditioning and Deflation, Leading to a New Deflation Space
Nicole Spillane, Daniel B Szyld
New convergence bounds are presented for weighted, preconditioned, and deflated GMRES for the solution of large, sparse, non-Hermitian linear systems. These bounds are given for th…
Analysis of Randomized Householder-Cholesky QR Factorization with Multisketching
Andrew J. Higgins, Daniel B. Szyld, Erik G. Boman +1
CholeskyQR2 and shifted CholeskyQR3 are two state-of-the-art algorithms for computing tall-and-skinny QR factorizations since they attain high performance on current computer archi…
Preconditioned Chebyshev BiCG for parameterized linear systems
Siobhán Correnty, Elias Jarlebring, Daniel B. Szyld
We consider the problem of approximating the solution to for many different values of the parameter . Here we assume is large, sparse, and nonsingular wit…
On the Convergence of Randomized and Greedy Relaxation Schemes for Solving Nonsingular Linear Systems of Equations
Andreas Frommer, Daniel B. Szyld
We extend results known for the randomized Gauss-Seidel and the Gauss-Southwell methods for the case of a Hermitian and positive definite matrix to certain classes of non-Hermitian…
On non-Hermitian positive (semi)definite linear algebraic systems arising from dissipative Hamiltonian DAEs
Candan Güdücü, Jörg Liesen, Volker Mehrmann +1
We discuss different cases of dissipative Hamiltonian differential-algebraic equations and the linear algebraic systems that arise in their linearization or discretization. For eac…
A posteriori superlinear convergence bounds for block conjugate gradient
Christian E. Schaerer, Daniel B. Szyld, Pedro J. Torres
In this paper, we extend to the block case, the a posteriori bound showing superlinear convergence of Conjugate Gradients developed in [J. Comput. Applied Math., 48 (1993), pp. 327…
Asynchronous Richardson iterations
Edmond Chow, Andreas Frommer, Daniel B. Szyld
We consider asynchronous versions of the first and second order Richardson methods for solving linear systems of equations. These methods depend on parameters whose values are chos…
Dynamic jamming of dense suspensions under tilted impact
Endao Han, Liang Zhao, Nigel Van Ha +3
Dense particulate suspensions can not only increase their viscosity and shear thicken under external forcing, but also jam into a solid-like state that is fully reversible when the…
A block Recycled GMRES method with investigations into aspects of solver performance
Michael L. Parks, Kirk M. Soodhalter, Daniel B. Szyld
We propose a block Krylov subspace version of the GCRO-DR method proposed in [Parks et al.; SISC 2005], which is an iterative method allowing for the efficient minimization of the…
Multipreconditioned GMRES for Shifted Systems
Tania Bakhos, Peter Kitanidis, Scott Ladenheim +2
An implementation of GMRES with multiple preconditioners (MPGMRES) is proposed for solving shifted linear systems with shift-and-invert preconditioners. With this type of precondit…
Preconditioned eigensolvers for large-scale nonlinear Hermitian eigenproblems with variational characterizations. II. Interior eigenvalues
Daniel B. Szyld, Eugene Vecharynski, Fei Xue
We consider the solution of large-scale nonlinear algebraic Hermitian eigenproblems of the form that admit a variational characterization of eigenvalues. These problems a…
Krylov Subspace Recycling for Sequences of Shifted Linear Systems
Kirk M. Soodhalter, Daniel B. Szyld, Fei Xue
We study the use of Krylov subspace recycling for the solution of a sequence of slowly-changing families of linear systems, where each family consists of shifted linear systems tha…
Asynchronous iterative computations with Web information retrieval structures: The PageRank case
Giorgos Kollias, Efstratios Gallopoulos, Daniel B. Szyld
There are several ideas being used today for Web information retrieval, and specifically in Web search engines. The PageRank algorithm is one of those that introduce a content-neut…