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THE SHAPE OF THE SYMMETRIC SOLUTION SET
 

Summary: - - - -
3
THE SHAPE OF THE SYMMETRIC
SOLUTION SET
Götz Alefeld*, Vladik Kreinovich**, and
Günter Mayer***
*Institut für Angewandte Mathematik, Universität Karlsruhe,
D-76128K arlsruhe, Germany, email goetz.alefeld@mathematik.uni-karlsruhe.de
**Department of Computer Seienee, University of Texas at EI Paso,
EI Paso, TX 79968, email vladik@cs.utep.edu
***Fachbereieh Mathematik, Universität Rostock,
D-18051 Rostoek, Germany, email guenter.mayer@mathematik.uni-rostoek.de
ABSTRACT
We give a. new deduction of the set of inequaJities whieh ehara.cterize the solution set
S of rea.llinear systems Ax = b with the n X n eoefficient matrix A varying between
a. lower bound A and an upper bound A, and with b similarly varying between !!.and
b. The idea. ofthis deduction ean also be used to eonstruct a. set of inequaJities which
deseribe the so--ca.lled symmetrie solution set Ssym, i.e., the solution set ofAx = b
with A = AT varying between the bounds A = AT and A = AT. This is the ma.in
result of our pa.per. We show that in eaeh orthant Ssym is the intersection of S with

  

Source: Alefeld, Götz - Institut für Angewandte und Numerische Mathematik & Fakultät für Mathematik, Universität Karlsruhe

 

Collections: Mathematics