Handbook of Linear Algebra, 2nd Edition

Chapter 64

Large-Scale Matrix Computations

Roland W. Freund

University of California, Davis

Computational problems, especially in science and engineering, often involve large matrices. Examples of such problems include large sparse systems of linear equations [FGN92], [Saa03], [vdV03], e.g., arising from discretizations of partial differential equations, eigenvalue problems for large matrices [BDD00], [LM05], linear time-invariant dynamical systems with large state-space dimensions [FF94], [FF95], [Fre03], and large-scale linear and nonlinear optimization problems [KR91], [Wri97], [NW99], [GMS05]. The large matrices in these problems exhibit special structures, such as sparsity, that can be exploited in computational procedures for their solution. ...