27th Conference of the International Linear Algebra Society (ILAS 2026)

Session

Krylov Iterative Methods for Linear Equations

MS 21

May 18, 2026, 11:00 AM

173. Krylov Methods for Rank-one Updates of Eigenvalue Problems and Linear Equations

Dona Ishara Saparamadu (Baylor University, Waco, Texas)

5/18/26, 11:00 AM

Krylov Iterative Methods for Linear Equations

Minisymposium Talk

Krylov methods are given for rank-one updates of both eigenvalue and linear equations problems. For eigenvalues, an Arnoldi iteration for the original matrix can be continued on the rank-one changed matrix. We discuss how careful implementation allows the desired accuracy to be attained for the updated matrix. Next, methods are given for linear equations, one that uses the updated Arnoldi...

304. Convergence Analysis for Infinite GMRES

Jordan Jackson (Virginia Tech)

5/18/26, 11:25 AM

Krylov Iterative Methods for Linear Equations

Minisymposium Talk

Many applications require the solution of large-scale linear systems that have nonlinear parameter dependence. The Infinite GMRES algorithm, developed by Jarlebring and Correnty in 2022, converts these systems into infinite-dimensional systems with linear parameter dependence. This transformation involves a linearization process that results in a system with a special companion-like structure....

375. Twin CG for Linear Equations with Multiple Right-hand Sides

Abigail Williams (Baylor University)

5/18/26, 11:50 AM

Krylov Iterative Methods for Linear Equations

Minisymposium Talk

A very simple approach to solving multiple right-hand side systems is proposed. For symmetric problems, the conjugate gradient method is a very efficient way to solve linear equations. We will use the same parameters from solving the first system for other systems. This is called Twin CG. It corresponds to applying the same polynomial to the other systems as was used for the first system. No...

317. Polynomial Preconditioning for Indefinite Matrices

Hayden Henson (Baylor University)

5/18/26, 2:00 PM

Krylov Iterative Methods for Linear Equations

Minisymposium Talk

Preconditioning plays a central role in accelerating the convergence of iterative methods for solving large linear systems. Among the various approaches, polynomial preconditioning offers a flexible approach. Krylov subspace methods provide a natural setting for constructing polynomials that can be used as preconditioners. In this work, we investigate the use of polynomial preconditioning...

310. Polynomial Preconditioned Golub-Kahan for Finding Singular Values and Solving Least Squares

Kingsley Michael (Baylor University)

5/18/26, 2:25 PM

Krylov Iterative Methods for Linear Equations

Minisymposium Talk

Golub-Kahan bidiagonalization procedure is well known for its role in computing singular values and solving least squares problems. We present a polynomial-preconditioned variant of this framework aimed at reducing the need for restarting and extensive orthogonalization. This talk outlines the formulation and motivation for the method and examines its potential to improve performance in...

357. Preconditioner Updating with Lasso-based Sparse Approximate Maps

Achintya Sunil

5/18/26, 2:50 PM

Krylov Iterative Methods for Linear Equations

Minisymposium Talk

Design problems such as topology optimization and PDE-based inverse problems require the solution of a sequence of linear-systems derived from finite element or finite difference discretization. Preconditioning is essential for the fast solution of these systems by iterative methods. However, computing an accurate preconditioner for every system in the sequence may be a computational...