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The Shape of the Symmetric Solution Set

  • Götz Alefeld
  • Vladik Kreinovich
  • Günter Mayer
Part of the Applied Optimization book series (APOP, volume 3)

Abstract

We give a new deduction of the set of inequalities which characterize the solution set S of real linear systems Ax = b with the n × n coefficient matrix A varying between a lower bound \(\underline A \) and an upper bound \(\overline A \), and with b similarly varying between \(\underline b \) and \(\overline b \). The idea of this deduction can also be used to construct a set of inequalities which describe the so-called symmetric solution set S sym, i.e., the solution set of Ax = b with A = A T varying between the bounds \(\underline A = {\underline A ^T}\) and \(\overline A = {\overline A ^T}.\) This is the main result of our paper. We show that in each orthant S sym is the intersection of S with sets of which the boundaries are quadrics.

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Götz Alefeld
    • 1
  • Vladik Kreinovich
    • 2
  • Günter Mayer
    • 3
  1. 1.Institut für Angewandte MathematikUniversität KarlsruheKarlsruheGermany
  2. 2.Department of Computer ScienceUniversity of Texas at El PasoEl PasoUSA
  3. 3.Fachbereich MathematikUniversität RostockRostockGermany

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