This article addresses the inference of physics models from data, from the perspectives of
inverse problems and model reduction. These fields develop formulations that integrate data …

This book on iterative methods for linear and nonlinear equations can be used as a tutorial
and a reference by anyone who needs to solve nonlinear systems of equations or large …

In an operating nuclear reactor core, various physical phenomena of different nature are
interrelated. Multi-physics calculations that account for the interrelated nature of the …

This small book on Newton's method is a user-oriented guide to algorithms and
implementation. Its purpose is to show, via algorithms in pseudocode, in MATLAB®, and …

This paper is about GMRES algorithms for the solution of nonsingular linear systems. We
first consider basic algorithms and study their convergence. We then focus on acceleration …

This book deals with numerical methods for solving large sparse linear systems of
equations, particularly those arising from the discretization of partial differential equations. It …

The problem of finding good preconditioners for the numerical solution of indefinite linear
systems is considered. Special emphasis is put on preconditioners that have a 2× 2 block …

Classical boundary integral equations arising from the potential theory and acoustics
(Laplace and Helmholtz equations) are derived. Using the parametrization of the boundary …

Radial Basis Function (RBF) methods have become the primary tool for interpolating
multidimensional scattered data. RBF methods also have become important tools for solving …

1. INTRODUCTION. We explain why Krylov methods make sense, and why it is natural to
represent a solution to a linear system as a member of a Krylov space. In particular we show …