References

Matrix multiplication

• Rump, S. M. (2010, July). Verification methods: Rigorous results using floating-point arithmetic. In Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation (pp. 3-4). pdf

• Ozaki, K., Ogita, T., Rump, S. M., & Oishi, S. I. (2012). Fast algorithms for floating-point interval matrix multiplication. Journal of Computational and Applied Mathematics, 236(7), 1795-1814. pdf

Linear systems

• Inner estimation of interval linear systems article

Eigenvalues

• Bounding the eigenvectors of symmetric interval matrices. Dr. N. P. Seif S. Hashem Prof. Dr. A. S. Deif.
• On the range of eigenvalues of an interval matrix. Jiri Rohn Assem Deif Assem Deif.
• Eigenvalues of symmetric interval matrices. Nikolay Stoyanov Kaleyski
• Computing the range of real eigenvalues of an interval matrix. Milan Hladik & David Daney.
• Bounds on Eigenvalues of Interval Matrices. Rohn, J.
• Hartman, David, Milan Hladík, and David Říha. "Computing the spectral decomposition of interval matrices and a study on interval matrix power." arXiv preprint arXiv:1912.05275 (2019). pdf
• Package https://github.com/dpsanders/IntervalEigenvalues.jl

Determinants

• https://arxiv.org/pdf/1809.03736.pdf

Others (sort me!)

• Numerical linear algebra using interval arithmetic. Hong Diep Nhuyen. THÈSE en vue de l’obtention du grade de Docteur de l’École Normale Supérieure de Lyon - Université de Lyon (2011).
• https://arxiv.org/pdf/1712.09940.pdf (rank)
• https://arxiv.org/pdf/1809.03736.pdf (determinant)
• https://www.sciencedirect.com/science/article/abs/pii/S0024379517306481 (inverse)