References

Matrix exponentiation

• Goldsztejn, Alexandre, and Arnold Neumaier. "On the Exponentiation of Interval Matrices." (2009).

• Frommer, Andreas, and Behnam Hashemi. "Computing enclosures for the matrix exponential." SIAM Journal on Matrix Analysis and Applications 41.4 (2020): 1674-1703. article

• Hartman, D., Hladík, M., & Říha, D. (2021). Computing the spectral decomposition of interval matrices and a study on interval matrix powers. Applied Mathematics and Computation, 403, 126174.

• Miyajima, Shinya. "Computing Enclosures for the Matrix Mittag–Leffler Function." Journal of Scientific Computing 87.2 (2021): 1-22.

• Frommer, Andreas, and Behnam Hashemi. "Algorithms with automatic result verification for the matrix exponential." XXI Householder Symposium on Numerical Linear Algebra. 2020.

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

• Shary, Sergey P. "A new method for inner estimation of solution sets to interval linear systems." Modeling, Design, and Simulation of Systems with Uncertainties. Springer, Berlin, Heidelberg, 2011. 21-42. 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

• Horáček, Jaroslav, Milan Hladík, and Josef Matějka. "Determinants of interval matrices." arXiv preprint arXiv:1809.03736 (2018). arxiv

Rank

• Rubei, Elena. "On rank range of interval matrices." Linear Algebra and its Applications 561 (2019): 81-97. arxiv

Inverse

• Rohn, Jiri, and Sergey P. Shary. "Interval matrices: Regularity generates singularity." Linear Algebra and its Applications 540 (2018): 149-159. article

Theses

• 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).