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

Session

Advances and Challenges in Eigensolvers

MS 26

May 18, 2026, 3:45 PM

292. The accuracy of the QZ algorithm and some tricks to improve it

Dr Thijs Steel (KU Leuven)

5/18/26, 3:45 PM

Advances and Challenges in Eigensolvers

Minisymposium Talk

For small and/or dense generalized eigenvalue problems, the QZ method remains the method of choice because of its robustness. In this talk, we will discuss how that robustness may occasionally fail, especially if the matrices are badly scaled or singular. We will discuss how new deflation criteria and some changes in the preprocessing can improve the robustness.

218. From eigenvector nonlinearities to eigenvalue nonlinearities

Vilhelm P. Lithell (KTH Royal Institute of Technology)

5/18/26, 4:10 PM

Advances and Challenges in Eigensolvers

Minisymposium Talk

We are interested in an eigenvector-nonlinear eigenvalue problem (NEPv), that is, a problem of the form $A(x)x=\lambda x$, where $A:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n\times n}$ is symmetric, and the eigenvector has a prescribed norm, for instance $\Vert x \Vert = 1$. In this sense, this class of problems generalize the linear eigenvalue problem. Motivated by applications such as the...

447. Fast Algorithms for Optimal Damping in Mechanical Systems

Francoise Tisseur (The University of Manchester)

5/18/26, 4:35 PM

Advances and Challenges in Eigensolvers

Minisymposium Talk

Optimal damping aims at determining a vector of damping coefficients $\nu$ that maximizes the decay rate of a mechanical system's response. This problem can be formulated as the minimization of the trace of the solution of a Lyapunov equation whose coefficient matrix depends on $\nu$. For physical relevance, the damping coefficients must be nonnegative and the resulting system must be...

492. From SCF to LOBPCG: Accelerated Solvers for Nonlinear Eigenvector Problems

Agnieszka Miedlar (Virginia Tech)

5/18/26, 5:00 PM

Advances and Challenges in Eigensolvers

Minisymposium Talk

This talk surveys modern iterative algorithms for solving large-scale nonlinear eigenvector problems, with a focus on both foundational methods and recent advances in nonlinear acceleration techniques. We examine SCF, FEAST, BPSD, and the LOBPCG eigenvector problems solvers, highlighting their theoretical foundations, practical performance, and applications. Through comparisons and...

453. The Restarted Block Two-Level Orthogonal Arnoldi Algorithm

Michael Jones

5/19/26, 3:45 PM

Advances and Challenges in Eigensolvers

Minisymposium Talk

The two-level orthogonal Arnoldi algorithm, abbreviated as TOAR, proposed by Lu, Su and Bai, is a Krylov method for the solution of large sparse quadratic eigenvalue problems (QEPs). Traditionally, such eigenproblems are first linearised with an appropriate companion form, then fed into the standard Arnoldi algorithm. This approach has the advantage of being simple, but suffers from large...

472. Integration of the GPLHR Method Within LS-DYNA

Daniel Bielich (Synopsys)

5/19/26, 4:10 PM

Advances and Challenges in Eigensolvers

Minisymposium Talk

LS-DYNA is a multiphysics simulation software package. It targets a wide range of industrial applications, such as modal analysis problems. These are solved with a variety of homegrown eigensolvers, tailored over decades to industrial models. In this talk, we will focus our attention on the quadratic eigenvalue problem underlying the rotational dynamics' framework of the Jeffcott Rotor model....

150. Inexact subspace projection methods for tensor eigenvalue problems

Alec Dektor (Lawrence Berkeley National Lab)

5/19/26, 4:35 PM

Advances and Challenges in Eigensolvers

Minisymposium Talk

I will present two projection methods for solving high-dimensional tensor eigenvalue problems with low-rank structure: an inexact Lanczos method and an inexact polynomial-filtered subspace iteration. The inexactness arises from low-rank compression, which enables efficient representation of high-dimensional vectors in low-rank tensor formats. A central challenge is that standard operations,...

376. Adaptive filtered subspace iteration for self adjoint eigenvalue problems on moving domains

Luka Grubisic (University of Zagreb, Faculty of Science, Department of Mathematics)

5/19/26, 5:00 PM

Advances and Challenges in Eigensolvers

Minisymposium Talk

Filtered subspace iterations can be used to approximate a finite cluster of eigenvalues of a lower semi-bounded selfadjoint operator in a Hilbert space. Prototype examples of such operators are Schrödinger operators with short-range potentials. A rational function (filter) of the operator is constructed such that the eigenspace of interest (eigenvalues below the infimum of the essential...