## Linear Algebra and its Applications (LAA) Special issue on Linear Algebra in Self-Validating Methods

The goal of self-validating methods is to compute correct results on digital computers - correct in a mathematical sense, covering all errors like representation, discretization, rounding errors or others.

These methods have a connection to linear algebra since problems are frequently transformed into linearized problems with uncertain data. Then the linearization and discretization errors are estimated, possibly together with an infinite dimensional part of the problem.

It has turned out that computation of an inclusion of the solution complex of even a linear system of equations with uncertain data is NP-hard. This has given rise to interesting connections between self-validating methods and complexity theory. Despite this, in many cases a reasonably sharp inclusion can be calculated. The class of problems being solvable in this sense has been extended in recent years.

The possibility to estimate the range of a function is a main ingredient of self-validating methods. Beside the naive way to get error bounds by replacing every operation by the corresponding interval operation, much more elaborate methods have come up using gradients, slopes, lp- and qp-approaches and more.

In the past few decades the area of self-validating methods has been evolving, with rapidly growing number of researchers. We want to take this opportunity to publish a special issue on self-validating methods. A preliminary list of topics would include:

• systems of linear equations and inequalities
• range of functions
• complexity theory for problems with uncertain data
• componentwise distance to singularity and/or stability
• sparse systems of equations
• algebraic eigenvalue problems
• iterative methods
• matrix methods in validation methods for differential equations
• use of M-matrices and H-matrices in validation methods
• analysis of zeros and connection to controllability
• combination of computer algebra with floating point methods.

This is a sample, but not an exclusive list of topics. If there is doubt about suitability of a particular paper, contact one of the editors of the special issue.

Please submit three (3) hard copies to one of the special issue editors listed below. The deadline for submission is September 30, 1999.

Jiri Rohn
Faculty of Mathematics and Physics
Charles University
Malostranske nam. 25
118 00 Prague
Czech Republic
e-mail rohn@uivt.cas.cz

Siegfried M. Rump
Inst. f. Computer Science III
Technical University Hamburg-Harburg
Eissendorfer Str. 38
21071 Hamburg, Germany
e-mail rump@tu-harburg.de

Tetsuro Yamamoto
Department of Mathematics
Faculty of Science
Ehime University
Matsuyama 790, Japan
e-mail yamamoto@dpc.ehime-u.ac.jp