ABSTRACT
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. Roughly speaking, computational problems involving matrices are called “large-scale” if they can be solved only by methods that exploit these special matrix structures.
