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

Session

Application-Driven Family of Matrix Computations: Factorization, Inverse, Linear Solve

MS 39

May 18, 2026, 3:45 PM

89. Scalable Approximate Selected Inversion via ILU and Spectral Corrections for Sparse Systems

Tahamina Akter (TU Braunschweig)

5/18/26, 3:45 PM

Application-Driven Family of Matrix Computations: Factorization, Inverse, Linear Solve

Minisymposium Talk

We analyze two parallel numerical strategies for computing selected entries of the matrix inverse of large, sparse, symmetric systems: The selected inverse method and a factorized approximate inverse method. Both techniques are aimed at computations via LU factorizations or incomplete LU (ILU) factorizations. The selected inverse approach exploits the LU/ILU factorization to recover the...

298. Matrix-Free Geometric Multigrid Preconditioning Of Combined Newton-GMRES For Solving Phase-Field Fracture With Local Mesh Refinement

Prof. Thomas Wick (Leibniz University Hannover)

5/18/26, 4:10 PM

Application-Driven Family of Matrix Computations: Factorization, Inverse, Linear Solve

Minisymposium Talk

In this talk, the matrix-free solution of quasi-static phase-field fracture problems is further investigated. More specifically, we consider a quasi-monolithic formulation in which the irreversibility constraint is imposed with a primal-dual active set method. The resulting nonlinear problem is solved with a line-search assisted Newton method. Therein, the arising linear equation systems are...

454. Loracx: Low Rank Approximations with Constraints at Exascale

Ramakrishnan Kannan

5/18/26, 4:35 PM

Application-Driven Family of Matrix Computations: Factorization, Inverse, Linear Solve

Minisymposium Talk

Analyzing large-scale scientific data—such as molecular dynamics simulations of $MoS_2$ recrystallization—poses significant challenges for traditional methods like Nonnegative Matrix Factorization (NMF), particularly on exascale systems. In this talk, we introduce Low-Rank Approximations with Constraints at Exascale (LORACX), a scalable framework that employs distributed, GPU-accelerated NMF...

446. Exploiting Kronecker Structure and Krylov Subspaces for Scalable Second-Order Optimization in Federated Physics-Informed Neural Networks

Amit Upadhyay (Indian Institute Of Technology (Indian School Of Mines) Dhanbad)

5/18/26, 5:00 PM

Application-Driven Family of Matrix Computations: Factorization, Inverse, Linear Solve

Minisymposium Talk

Solving partial differential equations (PDEs) using distributed Physics-Informed Neural Networks (PINNs) introduces major computational challenges associated with high-dimensional curvature estimation, ill-conditioned optimization landscapes, and communication overhead in federated environments. In this work, we exploit Kronecker structure and Krylov subspace methods to develop a scalable...