Froilán Martínez Dopico
Catedrático de Universidad
Área de Matemática Aplicada

Universidad Carlos III de Madrid
Departamento de Matemáticas
Avenida de la Universidad, 30
28911, Leganés, Madrid.

Teléfono: +34 91 624 9446
FAX: +34 91 624 9129
Despacho: 2.2.D.25 (Edificio Sabatini)
Scientific Publications

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 analysys 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. W. 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, 54 (2017), pp. 319-365. (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, SIAM Journal on Matrix Analysis and Applications, 38 (2017), pp. 249-272.
  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-González, 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.  (see related unpublished technical report in Unpublished Technical Reports section below)
  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, 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
  42. 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.
  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.

Other Scientific Publications (chapters of books, proceedings, papers in nonindexed journals...)

  1. F. M. Dopico, Feature Interview to Daniel Szyld, IMAGE (The Bulletin of the International Linear Algebra Society) 59, Fall 2017.
  2. F.M. Dopico, Book Review on Numerical Methods in Matrix Computations by Ảke Björck, SIAM Review, 58 (2016), pp. 363-365.
  3. F. De Terán, F.M. Dopico and D.S. Mackey, Linearizations of matrix polynomials: sharp lower bounds for the dimension and structures, Actas electrónicas del XXI C.E.D.Y.A/XI Congreso de Matemática Aplicada. Ciudad Real, 21-25 septiembre 2009.
  4. F.M. Dopico, Matemática Computacional: Un nuevo pilar para el desarrollo científico y tecnológico. Chapter in the book Matemáticas en la frontera: Nuevas infraestructuras matemáticas en la Comunidad de Madrid, Computación e Interacción I+D+i. Coordinadores: M. de León, J.L. González Llavona,A. Ibort y E. Zuazua. Pages 102 - 115. Comunidad de Madrid, Consejería de Educación (2007).
  5. J. Moro and F.M. Dopico, First Order Eigenvalue Perturbation Theory and the Newton Diagram. Chapter in the book Applied Mathematics and Scientific Computing, edited by Z. Drmac, V. Hari, L. Sopta, Z. Tutek and K. Veselic. Invited contribution for the Proceedings of the Second Conference
    on Applied Mathematics and Scientific Computing, held June 4-9, 2001 in Dubrovnik, Croatia. Pages 143-175. Kluwer Academic Publishers (2003).
  6. O.M. Bulashenko, L.L. Bonilla, J. Galán, J.A. Cuesta, F. C. Martínez-Dopico and J.M. Molera, Dynamics of Resonant Tunneling Domains in Superlattices: a Discrete Drift Model. Chapter in the book Quantum Transport in Ultrasmall Devices, D.K. Ferry, ed. Pages 501-504. Plenum Press (1995).
  7. L.L. Bonilla, J.A. Cuesta, J. Galán, F. C. Martínez-Dopico and J.M. Molera, Electric Field Domains in Superlattices: Dynamics. Chapter in the book 25 Years of Non-Equilibrium Statistical Mechanics. Proceedings of the XIII Sitges Conference. Sitges, Barcelona (Spain), 13-17 June 1994. J.J. Brey, J. Marro, J.M. Rubí, M. San Miguel ed. Pages 327-337. Springer-Verlag, Lectures Notes in Physics, Vol. 445 (1995).
  8. R. Merlin, S.H. Kwok, T.B. Norris, H.T. Grahn, K. Ploog, L.L. Bonilla, J. Galán, J.A. Cuesta, F. C. Martínez-Dopico and J.M. Molera, Dynamics of resonant tunneling domains in superlattices: theory and experiments. Chapter in the book Proceedings of the 22th International Conference on the Physics of
    Semiconductors, Vancouver, Canada, August 15-19, 1994, J. Lockwood, ed. Pages 1039-1042. World Scientific (1995).
  9. F. C. Martínez-Dopico and L.L. Bonilla, Estabilidad de soluciones incoherentes en un sistema hamiltoniano de osciladores acoplados. Actas del XIII C.E.D.Y.A./III Congreso de Matemática Aplicada. Madrid,13-15 de septiembre 1993. A. Casal, L. Gavete, C. Conde, J. Herranz ed. Pages 539-544. Universidad Politécnica de Madrid (1993).
  10. A. Loarte, F. C. Martínez-Dopico and M. Soler, Determination of \Xi_e from X-Ray observations of sawtooth heat pulse propagation in JET ohmic discharges, JET report (89) 28 (1989),  pp. 1-12.
  11. A. Loarte, F. C. Martínez-Dopico and M. Soler, TRANSP simulation of ohmic sawteeth in JET, JET report (89) 12 (1989), pp. 1-42.


Unpublished Technical Reports

  1. N. Castro-González, J. Ceballos, F.M. Dopico, and J. M. Molera, Multiplicative perturbation theory and accurate solution of least squares problems. Technical Report, 2012.