Copyright 2017 - Site designed and maintained by: Ariel Díaz De Armas

Catedrático de Universidad
(Full Professor)

Office: 2.2D25(Edificio Sabatini)
Phone: +34 916249446
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Curriculum Vitae

Click here to see more detailed information in my personal web page 

My research in Numerical Linear Algebra and Matrix Theory has been funded continuosly since the year 2000 as Principal Investigator of several research grants from the Ministerios de Educación y Ciencia, Ciencia y Tecnología, Ciencia e Innovación, and Economía y Competitividad of Spain. In addition, I have participated in several leading joint initiatives in Mathematics in Spain as, for instance, SIMUMAT and i-MATH Ingenio Mathematica. I am also member of the Spanish Network ALAMA for Linear Algebra, Matrix Analysis and its Applications.

I list only the most relevant research grants that  I have obtained as Principal Investigator in my career.

Research Grants as Principal Investigator 

  1. Structured Numerical Linear Algebra for Constant, Polynomial, and Rational Matrices. Ministerio de Economía y Competitividad of Spain. (Grant number: MTM2015-65798-P).  From January 1, 2016 until December 31, 2019. Number of members of the research team: 8. Budget: 45496 Euros + 1 four years long PhD Grant.
  2. Structured Numerical Linear Algebra: Matrix Polynomials, Special Matrices, and Conditioning. Ministerio de Econom ía y Competitividad of Spain. (Grant number: MTM2012-32542). From February 1, 2013 until December 31, 2015. Number of members of the research team: 8. Budget: 73710 Euros + 1 four years long PhD Grant.
  3. Numerical Linear Algebra: Theory, Structures and Algorithms. Ministerio de Ciencia e Innovación of Spain. (Grant number: MTM2009-09281). From January 1, 2010 until December 31, 2012. Number of members of the research team: 6. Budget: 37510.01 Euros.
  4. Accurate and stable algorithms in Numerical Linear Algebra. Ministerio de Educación y Ciencia of Spain. (Grant number: MTM2006-06671). From  October 1, 2006 until October 1, 2009. Number of members of the research team: 6. Budget: 49331.70 Euros.
  5. Matrix numerical algorithms for ill-conditioned structured spectral problems. Ministerio de Ciencia y Tecnología of Spain. (Grant number: BFM2003-00223). From December 1, 2003 until December 1, 2006. Number of members of the research team: 5. Budget: 39120 Euros.
  6. Orthogonal high relative accuracy algorithms for the symmetric eigenproblem. Ministerio de Ciencia y Tecnología of Spain. (Grant number: BFM2000-0008). From December 19, 2000 until December 19, 2003. Number of members of the research team: 3. Budget: 11000 Euros.

I have participated in other 12 Reseach Grants since the year 1991, among them I highlight the currently active one for funding partially the activities of ALAMA, that is, the Spanish Thematic Network on Linear Algebra, Matrix Analysis and Applications:

 

  • Thematic Network on Linear Algebra, Matrix Analysis and Applications. Ministerio de Economía y Competitividad of Spain. (Grant number: MTM2015-68805-REDT).  From December 1, 2015 until November 30, 2017. Number of members of the research team: 10. Budget: 35000 Euros. Principal Investigator: Ion Zaballa.

During the academic year 2016-2017, I am teaching one undergraduate and one graduate courses.


Undergraduate courses

  • Linear Algebra  (in English) de los Grados en Ingeniería de Sistemas Audiovisuales, Ingeniería de Sistemas de Comunicaciones e Ingeniería en Telemática (grupo magistral + grupo reducido).


Docencia en Máster en Ingeniería Matemática (Graduate Courses)

  • Métodos Avanzados en Análisis Matricial en el Máster en Ingeniería Matemática.

 

 

 

 

This list only includes some of the talks that I have presented. If you are interested in some talk that does not appear here, please contact me.

Fast and accurate computations with some classes of quasiseparable matrices. Invited talk in the Minisymposium on Quasiseparable Matrices and Polynomials in SIAM Conference on Applied Linear Algebra, Monterey, USA. October 26-29, 2009.

Papers in journals indexed in Journal Citation Reports (JCR) of Web of Science (Thomson Reuters)

  1. M.I. Bueno, F.M. Dopico, S. Furtado, and L. Medina, Conditioning and backward error of block-symmetric block-tridiagonal linearizations of matrix polynomials, submitted. (arXiv:1706.04150).
  2. F.M. Dopico and J. González-Pizarro, A compact rational Krylov method for large-scale rational eigenvalue problems,  submitted. (arXiv:1705.06982).
  3. A. Dmytryshyn and F.M. Dopico, Generic skew-symmetric matrix polynomials with fixed rank and fixed odd grade, submitted. (arXiv:1703.05797).
  4. F.M. Dopico, J. Pérez, and P. Van Dooren, Structured backward error analysis of linearized structured polynomial eigenvalue problems, submitted. (arXiv:1612.07011v1).
  5. P. Van Dooren and F.M. Dopico, Robustness and perturbations of minimal bases, Linear Algebra and its Applications, 2017, http://dx.doi.org/10.1016/j.laa.2017.05.011. (arXiv: 1612.03793).
  6. A. Dmytryshyn and F.M. Dopico, Generic matrix polynomials with fixed rank and fixed degree, submitted. (arXiv: 1612.04085).
  7. M.I. Bueno, F.M. Dopico, J. Pérez, R. Saavedra, and B. Zykoski, A unified approach to Fiedler-like pencils via strong block minimal bases pencils, submitted. (arXiv:1611.07170v1).
  8. A. Amparan, F.M. Dopico, S. Marcaida, and I. Zaballa, Strong linearizations of rational matrices, submitted. Available as MIMS-eprint 2016.51 of The University of Manchester.
  9. F. De Terán, F.M. Dopico, and J.M. Landsberg, An explicit description of the irreducible components of the set of matrix pencils with bounded normal rank, Linear Algebra and its Applications, 520 (2017), pp. 80-103. (arXiv:1606.02574)
  10. F.M. Dopico, P. Lawrence, J. Pérez, and P. Van Dooren, Block Kronecker linearizations of matrix polynomials and their backward errors, submitted. Extended version available as MIMS-eprint 2016.34 of The University of Manchester.
  11. F.M. Dopico and K. Pomés, Structured condition numbers for linear systems with parameterized quasiseparable coefficient matrices, Numerical Algorithms, 73 (2016), pp. 1131-1158 (DOI 10.1007/s11075-016-0133-8).
  12. N. Castro-González, F.M. Dopico, and J.M. Molera, Multiplicative perturbation theory of the Moore-Penrose inverse and the least squares problem, Linear Algebra and its Applications, 503 (2016), pp. 1-25.
  13. F. De Terán, F.M. Dopico, and J. Pérez, Eigenvalue condition numbers and pseudospectra of Fiedler matrices, Calcolo (2016). (DOI 10.1007/s10092-016-0189-9).
  14. B. Parlett, F. M. Dopico, and C. Ferreira, The inverse eigenvector problem for real tridiagonal matrices, SIAM Journal on Matrix Analysis and Applications, 37 (2016), pp. 577-597.
  15. F. De Terán and F. M. Dopico, Generic change of the partial multiplicities of regular matrix pencils under low-rank perturbations, SIAM Journal on Matrix Analysis and Applications, 37 (2016), pp. 823-835.
  16. F. M. Dopico and K. Pomés, Structured eigenvalue condition numbers for parameterized quasiseparable matrices, Numerische Mathematik, 134 (2016), pp. 473–512 (DOI 10.1007/s00211-015-0779-5).
  17. F. De Terán, F. M. Dopico, and P. Van Dooren, Constructing strong l-ifications from dual minimal bases, Linear Algebra and its Applications, 495 (2016), pp. 344-372.
  18. F. De Terán, F. M. Dopico, D. S. Mackey, and P. Van Dooren, Polynomial zigzag matrices, dual minimal bases, and the realization of completely singular polynomials, Linear Algebra and its Applications, 488 (2016), pp. 460-504.
  19. M. I. Bueno, F. M. Dopico, and S. Furtado, Linearizations of Hermitian matrix polynomials preserving the sign characteristic, to appear in SIAM Journal on Matrix Analysis and Applications.
  20. M. I. Bueno, F. M. Dopico, S. Furtado, and M. Rychnovsky, Large vector spaces of block-symmetric strong linearizations of matrix polynomials, Linear Algebra and its Applications, 477 (2015), pp. 165-210.
  21. F. M. Dopico, J. González, D. Kressner, and V. Simoncini, Projection methods for large-scale T-Sylvester equations, Mathematics of Computation, 85 (2016), pp. 2427-2455.
  22. F. De Terán, F. M. Dopico, and P. Van Dooren, Matrix polynomials with completely prescribed eigenstructure, SIAM Journal on Matrix Analysis and Applications, 36 (2015), pp. 302-328.
  23. F. De Terán, F. M. Dopico, and J. Pérez, Backward stability of polynomial root-finding using Fiedler companion matrices, IMA Journal of Numerical Analysis, 36 (2016), pp. 133-173.
  24. F. M. Dopico and F. Uhlig, Computing matrix symmetrizers, Part 2: new methods using eigendata and linear means; a comparison, Linear Algebra and its Applications, 504 (2016), pp. 590-622 .
  25. M. Dailey, F. M. Dopico, and Q. Ye, Relative perturbation theory for diagonally dominant matrices, SIAM Journal on Matrix Analysis and Applications, 35 (2014), pp. 1303-1328.
  26. M. Dailey, F. M. Dopico, and Q. Ye, A new perturbation bound for the LDU factorization of diagonally dominant matrices, SIAM Journal on Matrix Analysis and Applications, 35 (2014), pp. 904-930.
  27. F. De Terán, F. M. Dopico, and D. S. Mackey, Spectral equivalence of matrix polynomials and the index sum theorem, Linear Algebra and its Applications, 459 (2014), pp. 264-333.
  28. F. De Terán, F. M. Dopico, and J. Pérez, New bounds for roots of polynomials based on Fiedler companion matrices, Linear Algebra and its Applications, 451 (2014), pp. 197-230.
  29. F. M. Dopico, Alan Turing and the origins of modern Gaussian elimination, Arbor, Vol.189-764 (2013), a084. dx.doi.org/10.3989/arbor.2013.764n6007.
  30. N. Castro-Gonz ález, J. Ceballos, F. M. Dopico, and J. M. Molera, Accurate solution of structured least squares problems via rank-revealing decompositions, SIAM Journal on Matrix Analysis and Applications, 34 (2013), pp. 1112-1128.
  31. F. De Terán, F. M. Dopico, and J. Pérez, Condition numbers for inversion of Fiedler companion matrices, Linear Algebra and its Applications, 439, 944-981, (2013).
  32. F. De Terán, F. M. Dopico, and D. S. Mackey, Fiedler companion linearizations for rectangular matrix polynomials, Linear Algebra and its Applications, 437, 957-991 (2012).
  33. C. Ferreira, B. Parlett, and F. M. Dopico, Sensitivity of eigenvalues of an unsymmetric tridiagonal matrix, Numerische Mathematik, 122 (2012), pp. 527-555.
  34. F. De Terán, F. M. Dopico, N. Guillery, D. Montealegre, and N. Reyes, The solution of the equation \(AX+X^*B = 0\), Linear Algebra and its Applications, 438 (2013), pp. 2817-2860.
  35. F. M. Dopico, V. Olshevsky, and P. Zhlobich, Stability of QR-based fast system solvers for a subclass of quasiseparable rank one matrices, Mathematics of Computation, 82 (2013), pp. 2007-2034.
  36. F. De Terán and F. M. Dopico, Consistency and efficient solution of the Sylvester equation for *-congruence, Electronic Journal of Linear Algebra, 22 (2011), pp. 849-863.
  37. F. De Terán and F. M. Dopico, The equation \(XA+AX^* =0\) and the dimension of *-congruence orbits, Electronic Journal of Linear Algebra, 22 (2011), pp. 448-465.
  38. M. I. Bueno, F. De Terán and F. M. Dopico, Recovery of eigenvectors and minimal bases of matrix polynomials from generalized Fiedler linearizations, SIAM Journal on Matrix Analysis and Applications, 32 (2011), pp. 463-483.
  39. F. M. Dopico and J. M. Molera, Accurate solution of structured linear systems via rank-revealing decompositions, IMA Journal of Numerical Analysis, 32 (2012), pp.1096-1116 (doi:10.1093/imanum/drr023).
  40. F. M. Dopico and P. Koev, Perturbation theory for the LDU factorization and accurate computations for diagonally dominant matrices, Numerische Mathematik, 119 (2011), pp. 337-371 (DOI: 10.1007/s00211-011-0382-3).
  41. F. De Terán and F. M. Dopico, The solution of the equation \(XA+AX^T=0\) and its application to the theory of orbits,  Linear Algebra and its Applications, 434 (2011), pp. 44-67.
  42. F. De Terán, F. M. Dopico and D. S. Mackey, Palindromic companion forms for matrix polynomials of odd degree, Journal of Computational and Applied Mathematics, 236 (2011), pp. 1464-1480. Also available as MIMS EPRINT 2010.33
  43. F. De Terán, F. M. Dopico and D. S. Mackey, Fiedler companion linearizations and the recovery of minimal indices, SIAM Journal on Matrix Analysis and Applications, 31 (2010), pp. 2181-2204. Also available as MIMS EPRINT 2009.77.
  44. F. De Terán and F.M. Dopico, First order spectral perturbation theory of square singular matrix polynomials, Linear Algebra and its Applications, 432 (2010), pp. 892-910.
  45. F.M. Dopico, P. Koev and J. M. Molera, Implicit standard Jacobi gives high relative accuracy, Numerische Mathematik, 113 (2009), pp. 519-553.
  46. F. De Terán, F.M. Dopico and D. S. Mackey, Linearizations of singular matrix polynomials and the recovery of minimal indices, Electronic Journal of Linear Algebra 18 (2009), pp. 371-402.
  47. F.M. Dopico and C.R. Johnson, Parametrization of the matrix symplectic group and applications, SIAM Journal on Matrix Analysis and Applications, 31 (2009), pp. 650-673.
  48. F. De Terán and F.M. Dopico, Low rank perturbation of regular matrix polynomials, Linear Algebra and its Applications, 430 (2009), pp.579-586.
  49. F. De Terán and F.M. Dopico, Sharp lower bounds for the dimension of linearizations of matrix polynomials, Electronic Journal of Linear Algebra, 17 (2008), pp. 518-531.
  50. F.M. Dopico y P. Koev, Bidiagonal decompositions of oscillating systems of vectors, Linear Algebra and its Applications, 428 (2008), pp. 2536-2548.
  51. F. De Terán and F.M. Dopico, A note on generic Kronecker orbits of matrix pencils with fixed rank, SIAM Journal on Matrix Analysis and Applications, 30 (2008), pp. 491-496.
  52. F. De Terán, F.M. Dopico and J. Moro, First order spectral perturbation theory of square singular matrix pencils, Linear Algebra and its Applications, 429 (2008), pp. 548-576.
  53. E.S. Coakley, F.M. Dopico and C.R. Johnson, Matrices with orthogonal groups admitting only determinant one, Linear Algebra and its Applications, 428 (2008), pp. 796-813.
  54. F. De Terán, F.M. Dopico and J. Moro, Low rank perturbation of Weierstrass structure, SIAM Journal on Matrix Analysis and Applications, 30 (2008), pp. 538-547.
  55. P. Koev and F.M. Dopico, Accurate eigenvalues of certain sign regular matrices, Linear Algebra and its Applications, 424 (2007), pp. 435-447.
  56. F. De Terán and F.M. Dopico, Low rank perturbation of Kronecker structures without full rank, SIAM Journal on Matrix Analysis and Applications, 29 (2007), pp. 496-529.
  57. M. I. Bueno and F.M. Dopico, A more accurate algorithm for computing the Christoffel transformation, Journal of Computational and Applied Mathematics, 205 (2007), pp. 567-582.
  58. F.M. Dopico, C. R. Johnson and J. M. Molera, Multiple LU factorizations of a singular matrix, Linear Algebra and its Applications, 419 (2006), pp. 24-36.
  59. F.M. Dopico and P. Koev, Accurate symmetric rank revealing and eigendecompositions of symmetric structured matrices, SIAM Journal on Matrix Analysis and Applications, 28 (2006), pp. 1126-1156.
  60. F.M. Dopico and C. R. Johnson, Complementary bases in symplectic matrices and a proof that their determinant is one, Linear Algebra and its Applications, 419 (2006), pp. 772-778.
  61. F.M. Dopico and J. M. Molera, Perturbation theory for factorizations of LU type through series expansions, SIAM Journal on Matrix Analysis and Applications, 27 (2005), pp. 561-581.
  62. M.I. Bueno and F.M. Dopico, Stability and sensitivity of tridiagonal LU factorization without pivoting, BIT, 44 (2004), pp. 651-673.
  63. M.I. Bueno and F.M. Dopico, Stability and sensitivity of Darboux Transformation without parameter, Electronic Transactions on Numerical Analysis, 18 (2004), pp. 101-136.
  64. F.M. Dopico and J. Moro, A note on multiplicative backward errors of accurate SVD algorithms, SIAM Journal on Matrix Analysis and Applications, 25 (2004), pp. 1021-1031.
  65. J. Moro and F.M. Dopico, Low rank perturbation of Jordan structure, SIAM Journal on Matrix Analysis and Applications, 25 (2003), pp. 495-506.
  66. F.M. Dopico, J.M. Molera and J. Moro, An orthogonal high relative accuracy algorithm for the symmetric eigenproblem, SIAM Journal on Matrix Analysis and Applications, 25 (2003), pp. 301-351.
  67. F.M. Dopico and J. Moro, Perturbation theory for simultaneous bases of singular subspaces, BIT, 42 (2002), pp.84-109.
  68. F.M. Dopico, J. Moro and J.M. Molera, Weyl-type relative perturbation bounds for eigensystems of Hermitian matrices, Linear Algebra and its Applications, 309 (2000), pp. 3-18.
  69. F.M. Dopico, A note on sin\Theta theorems for singular subspace variations, BIT,40 (2000), pp. 395-403.
  70. S. H. Kwok, T.B. Norris, L.L. Bonilla, J. Galán, J.A. Cuesta, F. C. Martínez-Dopico, J.M. Molera, H.T. Grahn, K. Ploog, and R. Merlin, Domain wall kinetics and tunneling-induced instabilities in superlattices, Physical Review B, 51 (1995), pp. 10171-10174.
  71. F. C. Martínez-Dopico, J.A. Cuesta, J.M. Molera and R. Brito, Random versus deterministic two-dimensional traffic flow models, Physical Review E, 51 (1995), pp. R835-R838.
  72. J.M. Molera, F. C. Martínez-Dopico, J.A. Cuesta and R. Brito, Theoretical approach to two-dimensional traffic flow models, Physical Review E, 51 (1995), pp. 175-187.
  73. L.L. Bonilla, J. Galán, J.A. Cuesta, F. C. Martínez-Dopico and J.M. Molera, Dynamics of electric field domains and oscillations of the photocurrent in a simple superlattice model, Physical Review B, 50 (1994), pp. 8644-8657.
  74. J.A. Cuesta, F. C. Martínez-Dopico, J.M. Molera and A. Sánchez, Phase transitions in two-dimensional traffic flow models, Physical Review E, 48 (1993), pp. R4175-R4178.
  75. M. Soler, F. C. Martínez-Dopico and J.M. Donoso, Integral Kinetic Method for one dimension: The Spherical Case, Journal of Statistical Physics, 69 (1992), pp. 813-835.
  76. F. C. Martínez-Dopico and M. Soler, An integral numerical method for a nonlinear Fokker-Planck equation, European Journal of Mechanics B/Fluids, 11 (1992), pp. 555-572.

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