Formally Verified Conditions for Regularity of Interval Matrices
Inria Sophia Antipolis · 2010
We propose a formal study of interval analysis that con- centrates on theoretical aspects rather than on computational ones. In particular we are interested in conditions for regularity of interval ma- trices. An interval matrix is called regular if all scalar matrices included in the interval matrix have non-null determinant and it is called singu- lar 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.