My present research interests are Numerical Linear Algebra and Matrix Theory. More precisely, I have been working on the effect that Möbius transformations has on (homogeneous and non-homogeneous) condition numbers and backward errors of polynomial eigenvalue problems,  the solution of inverse rational problems and the quasi-triangularization of regular matrix polynomials in arbitrary fields. Previously, I did some research in the field of Algebraic Topology, specifically, in Discrete Morse Theory. 

Scientific publications

• L. M. Anguas, D. Barrios Rolanía,  On polynomial solutions of certain finite order ordinary differential equations, submitted (arXiv:2309.10059).

• L. M. Anguas, F. M. Dopico, R. Hollister and D. S. Mackey, Quasi-Triangularization of Matrix Polynomials over Arbitrary Fields, Linear Algebra and its Applications, 665 (2023), 61-106 (arXiv:2112.08229)

• L. M. Anguas, M. I. Bueno and F. M. Dopico, Conditioning and backward errors of eigenvalues of homogeneous matrix polynomials under Möbius transformations, Mathematics of Computation, 80, 322 (2020), 767-805 (arXiv:1810:11495).

• L. M. Anguas, M. I. Bueno and F. M. Dopico, A comparison of eigenvalue condition numbers for matrix polynomials, Linear Algebra and its Applications, 564 (2019), 170-200 (arXiv:1804.09825).

• L. M. Anguas, F. M. Dopico, R. Hollister and D. S. Mackey, Van Dooren’s index sum theorem and rational matrices with prescribed structural data, SIAM J. Matrix Anal. Appl. 40, 2 (2019), 720-738. (MIMS-eprint 2018.6 of The University of Manchester).