Sufficient Conditions for Regularity and Singularity of Interval Matrices
SIAM Journal on Matrix Analysis and Applications
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Journal of Functional Programming
Interactive Theorem Proving and Program Development
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ARITH '05 Proceedings of the 17th IEEE Symposium on Computer Arithmetic
Proving Bounds on Real-Valued Functions with Computations
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Verified Real Number Calculations: A Library for Interval Arithmetic
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Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
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TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Formal Verification of Exact Computations Using Newton's Method
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Interval Analysis for Certified Numerical Solution of Problems in Robotics
International Journal of Applied Mathematics and Computer Science - Verified Methods: Applications in Medicine and Engineering
A HOL theory of euclidean space
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Proving bounds for real linear programs in Isabelle/HOL
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
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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.