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Description

Computational problems, especially in science and engineering, often involve large matrices. Examples of such problems include large sparse systems of linear equations, e.g., arising from discretizations of partial differential equations, eigenvalue problems for large matrices, linear time-invariant dynamical systems with large state-space dimensions, and large-scale linear and nonlinear optimization problems. 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.

In this talk, I first give a brief introduction to large-scale matrix computations, and then present two current projects: Dimension reduction of truly large-scale systems of differential-algebraic equations, and iterative methods for the solution of extremely large linear systems of equations arising in power grid analysis of very large-scale integrated (VLSI) circuits.