New paper on arXiv detailing a new solution method for NEPs and Resonance Problems
arXiv Link here
Conference Website here
I was blessed to recieve an NSF Graduate Research Fellowship in 2022. Special thanks to Dr. David Brown and Dr. Jia Zhao of Utah State University, Dr. Jim Nagy of Emory University, and Dr. Jun Kitagawa of Michigan State.
Finally meeting up with friends from the 2021 Emory REU. You can checkout the REU here
Published in SIURO, 2021
A convergence analysis of a finite difference scheme for the 1-D Parabolic Optimal Transport Problem.
Recommended citation: Brauer A, Krawick M, and Santana M. (2021). "Numerical Analysis of the 1-D Parabolic Optimal Transport Problem." SIAM SIURO. Vol 14:150-166.
Published in SIURO, 2022
Devising an algorithm for Computed Tomography with unknown view angles and distance from the x-ray source to the object.
Recommended citation: Huynh M, Santana M. (2022). "Alternating Minimization for Computed Tomography with Unknown Geometry Parameters." SIURO. Vol 15:62-76.
Published in Journal of Algebra Combinatorics Discrete Structures and Applications, 2022
Study of cordial labeling of directed graphs
Recommended citation: Beasley L, Santana M, Mousley J, and Brown D. (2022). " Cordiality of Digraphs " Journal of Algebra Combinatorics Discrete Structures and Applications. Vol 10:1.
Published in Preprint, 2024
We take a rational approach to the nonlinear eigenvalue problem
Recommended citation: O. P. Bruno, M. A. Santana, L. N. Trefethen (2024). " Evaluation of Resonances via AAA Rational Approximation of Randomly Scalarized Boundary Integral Resolvents " arXiv:2405.19582 .
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Linear Algebra, Utah State University, Department of Mathematics, 2021
Lead four recitations a week for an introductory linear algebra course and held office hours. I also created a jupyter notebook to demonstrate image compression using singular value decomposition. Major topics included solving linear systems, projections, orthogonal basises, eigenvalues, diagonalization, singular value decomposition, and general linear operators.