Formally Verified Conditions for Regularity of Interval Matrices

  • Ioana Paşca
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6167)

Abstract

We propose a formal study of interval analysis that concentrates on theoretical aspects rather than on computational ones. In particular we are interested in conditions for regularity of interval matrices. An interval matrix is called regular if all scalar matrices included in the interval matrix have non-null determinant and it is called singular otherwise. Regularity plays a central role in solving systems of linear interval equations. Several tests for regularity are available and widely used, but sometimes rely on rather involved results, hence the interest in formally verifying such conditions of regularity. In this paper we set the basis for this work: we define intervals, interval matrices and operations on them in the proof assistant Coq, and verify criteria for regularity and singularity of interval matrices.

Keywords

interval analysis regularity of interval matrices formal verification Coq SSReflect 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Ioana Paşca
    • 1
  1. 1.INRIA Sophia Antipolis 

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