Linear Algebra, Numerical

Synonyms

Matrix computations

Definition

Numerical linear algebra (or matrix computations) is the design and analysis of matrix operations and algorithms. Matrix computations plays a vital role in enabling the majority of computational science and engineering applications. Examples of such applications include: computational fluid dynamics, structural mechanics, fluid-structure interaction, computational electromagnetics, image processing, web search (PageRank), and information retrieval, just to list a few. Matrix computations can be divided into two classes: (a) dense matrix computations, and (b) sparse matrix computations, with the former being rich in data locality and hence can readily achieve high performance on modern architectures. The basic standard problems in numerical linear algebra are: (i) solving linear systems of equations, (ii) solving linear least squares problems with or without constraints, (iii) solving standard and generalized eigenvalue problems, and (iv)...