The Harwell Subroutine Library (HSL) is a renowned suite of efficient and robust numerical algorithms designed to tackle complex mathematical problems such a...

We introduce an iterative solver named MINARES for symmetric linear systems $Ax \approx b$, where $A$ is possibly singular. MINARES is based on t...

This paper presents $\texttt{Krylov.jl}$, a Julia package that implements a collection of Krylov processes and methods for solving a variety of linear pr...

We introduce an iterative method named GPMR for solving 2X2 block unsymmetric linear systems. GPMR is based on a new process that reduces simultaneously...

This paper presents an efficient method for extracting the second-order sensitivities from a system of implicit nonlinear equations. We design a custom aut...

We introduce iterative methods named TriCG and TriMR for solving symmetric quasi-definite systems based on the orthogonal tridiagonalization process proposed...

We present ExaPF.jl, a solver for power flow on GPUs, entirely written in Julia. It implements a highly parallel Newton-Raphson solver for nonlinear equati...

We introduce an iterative method named BiLQ for solving general square linear systems $Ax=b$ based on the Lanczos biorthogonalization process defined by ...