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 ...