Finite difference methods continue to provide an important and parallelisable approach to many numerical simulations problems. Iterative multigrid and multilevel algorithms can co...
One of the most widely used methods for eigenvalue computation is the QR iteration with Wilkinson’s shift: here the shift s is the eigenvalue of the bottom 2 × 2 principal mino...
Ricardo S. Leite, Nicolau C. Saldanha, Carlos Tome...
Cyclic coordinate descent is a classic optimization method that has witnessed a resurgence of interest in machine learning. Reasons for this include its simplicity, speed and stab...
The asymptotic convergence of parameterized variants of Newton's method for the solution of nonlinear systems of equations is considered. The original system is perturbed by a...
Nicholas I. M. Gould, Dominique Orban, Annick Sart...
We introduce a new preconditioner for solving a symmetric Toeplitz system of equations by the conjugate gradient method. This choice leads to an algorithm which is particularly sui...