Faculty

Javier Perez Alvaro

Javier Perez Alvaro

Visiting Assistant Professor

Office: Math 205A
Email: javier.perez-alvaro@mso.umt.edu
Office Hours:

Monday: 10:00-10:50

Tuesday: 10:00-10:50

Wednesday: 2:00-3:00pm

Friday: 2:00-3:00pm

If these times don't work for you, please contact me to make an appointment.


Curriculum Vitae

Courses

M171 (calculus 1)

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.

Publications

  1. Explicit block-structures for block-symmetric Fiedler-like pencils, with Maribel Bueno, M. Martin, A. Song, and I. Viviano                                                                                                              
  2. Mixed forward-backward stability of the two-level orthogonal Arnoldi method for quadratic problems, with Karl Meerbergen.
  3. Structured backward error analysis of linearized structured polynomial eigenvalue problems, with Froilan M. Dopico and Paul Van Dooren.

  4. A simplified approach to Fiedler-like pencils via strong block minimal bases pencils,  with Maribel Bueno, Froiian M. Dopico, R. Saavedra and B. Zykoski.

  5. Block Kronecker Linearizations of Matrix Polynomials and their Backward Errors, with Piers W. Lawrence, Froilan M. Dopico, and Paul Van Dooren.

  6. Symmetric and skew-symmetric block Kronecker linearizations, with Heike Fassbender, and Nikta Shayanfar.

  7. Constructing strong linearizations for matrix polynomials in the Chebyshev bases, with Piers W. Lawrence.

  8. Pseudospectra and eigenvalue condition numbers of Fiedler matrices, with Fernando De Teran and Froilan M. Dopico.

  9. Fiedler-comrade and Fiedler-Chebyshev pencils, with Vanni Noferini.

  10. Chebyshev rootfinding via computing eigenvalues of colleague matrices: when is it stable? with Vanni Noferini.

  11. Backward stability of polynomial root-finding using Fiedler companion matrices, with Fernando De Teran, and Froilan M. Dopico.

  12. Technical report on backward stability of polynomial root-finding using Fiedler companion matrices, with Fernando De Teran, and Froilan M. Dopico.

  13. New bounds for roots of polynomials based on Fiedler companion matrices, with Fernando De Teran, and Froilan M. Dopico.

  14. Condition numbers for inversion of Fiedler companion matrices, with Fernando De Teran, and Froilan M. Dopico.