Parallel matrix algorithms and applications

摘要

The main focus of this special issue is on parallel matrix algorithms, a subject of crucial importance for numerical simulations, in which solving large linear algebra problems arises frequently. The numerical simulation process can be decomposed in five phases: (i) an application analysis, which defines the problem and expresses it as a set of mathematical equations that need to be solved; (ii) a mathematical study, which re-formulates the problem and supplements it with additional assumptions ensuring that it is well-posed; (iii) a numerical study, which defines approximation scheme that allows to solve the problem to a given precision; (iv) an algorithmic development, which implements the scheme on a computing platform; (v) a post-treatment, which analyzes and interprets the results. The fourth step, which is at the heart of this special issue, involves often numerous matrix problems arising, for instance, whenever a solution of a large set of linear equations or a computation of eigenvalues and/or eigenvectors is needed.