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Courses Taught

M461/M561 Data Science Analytics

M460/M540 Numerical Analysis

M220 Intro to Linear Algebra

Research Interests

My main interest are Matrix Analysis and Numerical Linear Algebra and its applications. These fields are a fundamental part of Numerical Analysis, Scientific Computing, and Computational Mathematics. More specifically my interests include (i) polynomial eigenvalue problems, matrix polynomials, and their linearizations; (ii) conditioning and backward error analyses; (iii) nonlinear eigenvalue problems.

Selected Publications

My main research interest is Numerical Linear Algebra and, more specifically solving . A nonlinear eigenvalue problem consits in finding scalars λ and nonzero vectors x such that

A(λ)x=0

Here A(λ)  is an  n×n matrix whose entries depend analytically on λ. The scalar λ is called an eigenvalue of A, and x is the corresponding eigenvector. This type of problems arise in a wide variety of science and engineering applications, such as the dynamic analysis of mechanical systems, the linear stability of flows in fluid mechanics, the stability analysis of time-delay systems, and electronic band structure calculations for photonic crystals, etc.

In , we have developed a new nonlinear eigenvalue solver that uses the recent to approximate the nonlinear eigenvalue problem by a rational eigenvalue problem. The resulting rational eigenvalue problem is solved by using and , allowing to efficiently solve large scale nonlinear eigenvalue problems. Our algorithm is competitive with , and  obtains the same accuracy but with less effort for the user. 

Publications

1. , with Maria C. Quintana
4. , with Froilán M. Dopico and Paul Van Dooren. 
5. , with Pieter Lietaert, Bart Vandereycken, and Karl Meerbergen.                                    
6. , with Maribel Bueno, M. Martin, A. Song, and I. Viviano. To appear in Electronic Journal of Linear Algebra, 2018.                                                                        
7. , with Karl Meerbergen. Linear Algebra and its Applications, 553, pp. 1-15, 2018.
8. , with Froilán M. Dopico and Paul Van Dooren. To appear in Mathematics of Computation, 2017.
9. ,  with Maribel Bueno, Froilán M. Dopico, R. Saavedra and B. Zykoski. Linear Algebra and its Applications, 547, pp. 45-104, 2018.
10. with Piers W. Lawrence, Froilán M. Dopico, and Paul Van Dooren. To appear in Numerische Mathematik, 2017.
11. , with Heike Fassbender, and Nikta Shayanfar. Technical report.  Available as arXiv:1606.01766.
12. , with Piers W. Lawrence. SIAM Journal on Matrix Analysis and Applications, 37(4), pp. 1600-1624, 2016.
13. , with Fernando De Terán and Froilán M. Dopico. Calcolo, 54(1), pp. 319-365, 2017.
14. , with Vanni Noferini. SIAM Journal on Matrix Analysis and Applications, 37(4), pp. 1600-1624, 2016.
15.  with Vanni Noferini. Mathematics of Computations, 86(306), pp. 1741-1767, 2016.
16. , with Fernando De Terán, and Froilán M. Dopico. IMA Journal of Numerical Analysis, 36, pp. 133-173, 2015.
17. , with Fernando De Terán, and Froilán M. Dopico. Technical report. Available as MIMS EPrint 2014.38, 2014.
18. , with Fernando De Terán, and Froilán M. Dopico. Linear Algebra and its Applications, 451, pp. 197-230, 2014.
19. , with Fernando De Terán, and Froilán M. Dopico. Linear Algebra and its Applications, 439, pp. 944-981, 2013