Some uses of the Lanczos algorithm (and why it works!)

Prof. Anne Greembaun

Courant Institute, New York University

The Lanczos algorithm can be used for many purposes besides its original application to solving eigenproblems. For example, it can be used to solve symmetric linear systems and to compute the exponential of a symmetric matrix. We show why the method is near optimal (among a class of methods) for such problem, even under the effects of finite precision arithmetic. This is joint work with Vladimir Druskin and Leonid Knizhnerman.