Rohn-abstract

Invited Talk

Linear Algebraic Problems with Inexact Data

J. Rohn
Charles University
Prague, Czech Republic rohn@cs.cas.cz

Abstract
This is a survey-type talk on linear interval equations and related topics which features the cornerstone points of the developments in this area in the 1990s, and also brings some new results. The topics selected include (i) the general result [Ro47], (ii) NP-hardness of the problem [Ro72], (iii) the enclosure algorithm by Hansen et al. [Ha], (iv) a new overestimation algorithm, (v) summary and some open problems.

The talk is intended to be accessible to a general mathematical audience, so that no preliminary knowledge except basic linear algebra is assumed.

[Ro47] J. Rohn: "Systems of linear interval equations",
Linear Algebra and Its Applications, 126:39--78, 1989.

[Ro72] J. Rohn and V. Kreinovich: "Computing exact componentwise bounds on solutions of linear systems with interval data is {NP}-hard",
SIAM Journal on Matrix Analysis and Applications, 16:415--420, 1995.

[Ha] E. R. Hansen: "Bounding the solution of interval linear equations",
SIAM Journal on Numerical Analysis, 29:1493--1503, 1992.