Froilán C. Martínez Dopico
Catedrático de Universidad

Research Grants
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 iMATH 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
 Structured Numerical Linear Algebra for Constant, Polynomial, and Rational Matrices. Ministerio de Economía y Competitividad of Spain. (Grant number: MTM201565798P). 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.
 Structured Numerical Linear Algebra: Matrix Polynomials, Special Matrices, and Conditioning. Ministerio de Econom ía y Competitividad of Spain. (Grant number: MTM201232542). 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.
 Numerical Linear Algebra: Theory, Structures and Algorithms. Ministerio de Ciencia e Innovación of Spain. (Grant number: MTM200909281). From January 1, 2010 until December 31, 2012. Number of members of the research team: 6. Budget: 37510.01 Euros.
 Accurate and stable algorithms in Numerical Linear Algebra. Ministerio de Educación y Ciencia of Spain. (Grant number: MTM200606671). From October 1, 2006 until October 1, 2009. Number of members of the research team: 6. Budget: 49331.70 Euros.
 Matrix numerical algorithms for illconditioned structured spectral problems. Ministerio de Ciencia y Tecnología of Spain. (Grant number: BFM200300223). From December 1, 2003 until December 1, 2006. Number of members of the research team: 5. Budget: 39120 Euros.
 Orthogonal high relative accuracy algorithms for the symmetric eigenproblem. Ministerio de Ciencia y Tecnología of Spain. (Grant number: BFM20000008). From December 19, 2000 until December 19, 2003. Number of members of the research team: 3. Budget: 11000 Euros.
I have participated in other 13 Research Grants since the year 1991, among them I highlight the ones 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: MTM201568805REDT). From December 1, 2015 until November 30, 2017. Number of members of the research team: 10. Budget: 35000 Euros. Principal Investigator: Ion Zaballa.
 Thematic Network on Linear Algebra, Matrix Analysis and Applications. Ministerio de Ciencia, Innovación y Universidades of Spain. (Grant number: MTM201790682REDT). From July 1, 2018 until June 30, 2020. Number of members of the research team: 10. Budget: 12000 Euros. Principal Investigator: José Mas.
Teaching
During the academic year 20182019, I am teaching two undergraduate and one graduate courses.
Undergraduate courses
 Álgebra Lineal del Grado en Ingeniería Electrónica Industrial y Automática (grupo magistal + grupo reducido).
 Cálculo Numérico del Grado en Ingeniería en Tecnologías Industriales (grupo magistal + grupo reducido).
Docencia en Máster en Ingeniería Matemática (Graduate Courses)

Álgebra Lineal Numérica en el Máster en Ingeniería Matemática.
Talks
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.
 Matrix polynomials with bounded rank and degree: generic eigenstructures and explicit descriptions. Invited talk in INdAM (Istituto Nazionale di Alta Matematica) Meeting "Structured Matrices in Numerical Linear Algebra: Analysis, Algorithms and Applications", Cortona, Italy. September 48, 2017.
 Paul Van Dooren's Index Sum Theorem and the solution of the inverse rational eigenvalue problem. Invited talk in Minisymposium "Matrix Polynomials" in "21st Conference of the International Linear Algebra Society", Iowa State University, Ames, Iowa, USA, July 2428, 2017
 Polynomial eigenvalue problems: linearizations and global backward error analysis. Plenary talk as "Keynote Speaker" in "4th International Symposium on Riordan Arrays and Related Topics", Universidad Complutense de Madrid, Spain, July 1720, 2017
 Strong linearizations of rational matrices: definition, explicit constructions, and associated recovery procedures. Invited talk in "Householder Symposium XX on Numerical Linear Algebra", Virginia Tech, Blacksburg, Virginia, USA, June 1823, 2017.
 Global backward error analysis of polynomial eigenvalue problems. Plenary talk in HPCSE 2017 ("High Performance Computing in Science and Engineering Conference"), Hotel Solán, Czech Republic, May 2225, 2017.
 Strong linearizations of rational matrices: theory and explicit constructions. Invited talk in the Conference "Numerical Linear Algebra and Applications (NLA2)", Centre International de Rencontres Mathématiques (CIRM), Luminy, Marseille, France, October 2428, 2016.
 Global backward error analyses for polynomial eigenvalue problems solved via linearizations. Invited talk in Minisymposium "Matrix Structures and Univariate Polynomial Rootfinding" in "20th Conference of the International Linear Algebra Society", KU Leuven, Leuven, Belgium, July 1115, 2016.
 Paul Van Dooren's index sum theorem: to infinity and beyond. Invited talk in Colloquium in honor of Paul Van Dooren on becoming Emeritus Professor. Université catholique de Louvain, LouvainlaNeuve, Belgium, July 8, 2016.
 Backward stability of polynomial rootfinding using Fiedler companion matrices and pencils. Invited talk in "Seminario MATESCO" of Departamento de Matem áticas, Estad í stica y Computaci ón de la Universidad de Cantabria. Facultad de Ciencias, Santander, Spain, November 16, 2015.
 Recent advances on inverse problems for matrix polynomials: the inverse rowdegree problem for dual minimal bases. Invited talk in "Minisymposium on Polynomial Eigenvalue Problems" in "SIAM Conference on Applied Linear Algebra", Hyatt Regency Atlanta, Atlanta, Georgia, USA, October 2630, 2015.
 Structured linearizations that preserve the sign characteristis of Hermitian matrix polynomials. Invited talk in Minisymposium "Nonlinear Eigenvalue Problems" in "8th International Congress on Industrial and Applied Mathematics (ICIAM 2015)", Beijing, China, August 1014, 2015.
 Relative perturbation theory for diagonally dominant matrices. Invited talk in Minisymposium "Perturbation theory for linear/nonlinear eigenvalue problems in action" in "8th International Congress on Industrial and Applied Mathematics (ICIAM 2015)", Beijing, China, August 1014, 2015.
 Polynomial Zigzag matrices, dual minimal bases, and applications. Invited Talk in Thematic Session "Structured Linear Algebra" in International Workshop on Operator Theory and Applications (IWOTA 2015), Tbilisi, Georgia, July 610, 2015.
 Volker Mehrmann and modern factorizations of symplectic matrices. Talk in "Numerical Algebra, Matrix Theory, DifferentialAlgebraic Equations, and Control Theory", Conference in Honor of Volker Mehrmann on the occasion of his 60th birthday, Technische Universität Berlin, Germany. May 69, 2015
 Backward stability of polynomial rootfinding using Fiedler companion matrices. Invited Talk in International Conference on Structured Numerical Linear and Multilinear Algebra: Analysis, Algorithms and Applications. Kalamata (Greece). September 812, 2014.
 Sylvester equations and the matrix symmetrizer problem. Invited Talk in "Minisymposium on Solution of Sylvesterlike Equations and Canonical Forms" in 19th Conference of the International Linear Algebra Society, Sungkyunkwan University, Se ul Campus, South Korea. August 69, 2014.
 Matrix polynomials with completely prescribed eigenstructure. Joint ALAMAGAMM/ANLA 2014 Meeting, Universitat Politècnica de Catalunya, Barcelona, July 1416, 2014.
 The inverse complex eigenvector problem for real tridiagonal matrices. Invited Talk in Special session "Linear Algebra: Algorithms and Applications", First Joint International Meeting RSMESCMSEMASIMAIUMI, Universidad del País Vasco, Bilbao, June 30July 4, 2014.
 Diagonally dominant matrices: Surprising recent results on a classical type of matrices. Numerical Analysis & Scientific Computing Seminars, School of Mathematics, The University of Manchester, April 29, 2014.
 The general inverse matrix polynomial index structure problem. Manchester Workshop on Nonlinear Eigenvalue Problems, The University of Manchester, UK, April 2325, 2014.
 Highly accurate Numerical Linear Algebra. Invited plenary talk in XXIII CEDYA/XIII CMA (XXIII Congreso de Ecuaciones Diferenciales y AplicacionesXIII Congreso de Matemática Aplicada), Universitat Jaume I, Castelló de la Plana, Spain, September 913, 2013.
 Structured eigenvalue condition numbers for parameterized quasiseparable matrices. Talk in 18th Conference of the International Linear Algebra Society, Providence, RI, USA. June 37, 2013.
 The matrix Sylvester equation for congruence. Invited talk at the School of Mathematics, University of Edinburgh, Scotland, February 7, 2013.
 Structured eigenvalue condition numbers for parameterized quasiseparable matrices. Invited Plenary Talk in International Conference on Numerical Linear Algebra and its ApplicationsNLAA 2013, IIT Guwahati, Assam, India, January 1518, 2013.
 Alan Turing and the origins of modern Gaussian elimination. Invited talk in International Symposium: The Alan Turing Legacy, Fundaci ón Ram ón Areces, Madrid, España, October 2324, 2012.
 Inverses and condition numbers of Fiedler companion matrices. Invited talk in Linear Algebra and its Applications Editorial Board (current & former) 2012 Meeting on the occasion of Hans Schneider's retirement as an EditorinChief of LAA, University of Wisconsin, Madison, USA, October 1014, 2012.
 Structured eigenvalue condition numbers for parameterized quasiseparable matrices. Invited talk in International Workshop on Structured Numerical Linear and Multilinear Algebra Problems: Analysis, Algorithms, and Applications, KU Leuven, Leuven, B elgium, September 1014, 2012.
 Structured perturbation theory for diagonally dominant matrices. Talk in 3rd Meeting on Linear Algebra, Matrix Analysis, and Applications, ALAMA 2012, Leganés, Spain, June 2729, 2012
 Highly accurate numerical linear algebra via rank revealing decompositions. Invited Talk in "Minisymposium: Different perspectives on conditioning and numerical stability" in 2012 SIAM Conference on Applied Linear Algebra, Valencia, Spain, June 1822, 2012.
 Diagonally dominant matrices: Surprising recent results on a classical class of matrices. Intergroups seminars. Department of Mathematics. Universidad Carlos III de Madrid. March 21, 2012.
 Recovery of eigenvectors of Matrix Polynomials from generalized Fiedler linearizations. Invited talk in Special Session on Structured Linear Algebra in SC2011International Conference on Scientific Computing, S. Margherita di Pula, Sardinia, Italy. October 1014, 2011
 Consistency and efficient solution of the Sylvester equation for *congruence: \(AX+X^* B = C\). Talk in the XXII CEDYA / XII CMA, XII Congreso de Matem ática Aplicada, Palma de Mallorca, Spain. September 59, 2011.
 Consistency and efficient solution of the Sylvester equation for congruence: \(AX+X^* B = C\). Talk in the 17th Conference of the International Linear Algebra Society, Braunschweig, Germany. August 2226, 2011.
 Structured perturbation theory for diagonally dominant matrices and numerical applications. Invited talk in Minisymposium: Structured Matrices: Applications, Theory, and Algorithms in the 7th International Congress on Industrial and Applied Mathematics (ICIAM2011), Vancouver, Canada. July 1822, 2011.
 Recent results on Fiedler linearizations for matrix polynomials. Invited talk in Thematic Minisymposium: Nonlinear Eigenvalue Problems in the 7th International Congress on Industrial and Applied Mathematics (ICIAM2011), Vancouver, Canada. July 1822, 2011.
 Structured perturbation theory of diagonally dominant matrices and numerical applications. Talk in Householder Symposium XVIII on Numerical Linear Algebra, Tahoe City, California. June 1217, 2011
 Generic spectral perturbation results for matrix polynomials. Invited talk in the Miniisimposium on Nonlinear Eigenvalue Problems in 16th Conference of the International Linear Algebra Society, Pisa, Italy. June 2125, 2010.
 Structured perturbation theory of LDU factorization and accurate computations for diagonally dominant matrices. Invited talk in the Minisymposium on Structured Matrices in 16th Conference of the International Linear Algebra Society, Pisa, Italy. June 2125, 2010.
 Perturbation theory of LDU factorization and accurate computations for diagonally dominant matrices. Talk in 2º Encuentro de Álgebra Lineal, Análisis Matricial y Aplicaciones, ALAMA2010, Valencia, Spain. June 24, 2010.
 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 2629, 2009.
 Perturbation theory for the LDU factorization of diagonally dominant matrices and its application to accurate computation of singular values. Talk in the SIAM Conference on Applied Linear Algebra, Monterey, USA. October 2629, 2009.
 Fast and accurate computations with totally nonnegative quasiseparable matrices. Invited talk in the Special Session Total Positivity of the Third Multidisciplinary International Symposium on Positive Systems: Theory and Applications, Valencia, Spain, September 24, 2009.
 Doubly structured sets of symplectic matrices. Invited Talk at Conference on Structured Linear Algebra Problems: Analysis, Algorithms and Applications, Cortona, Italy, September 1519, 2008.
 Implicit Jacobi algorithms for the symmetric eigenproblem. Invited Plenary Talk at 15th International Linear Algebra Society Conference, Cancún, México, June 1620, 2008.
 Implicit standard Jacobi gives high relative accuracy on rank revealing decompositions. Invited Plenary Talk at VII International Workshop on Accurate Solution of Eigenvalue Problems, CAAS, Dubrovnik, Croatia, June 912, 2008.
 An orthogonal and symmetric high relative accuracy algorithm for the symmetric eigenproblem. Invited Plenary Talk at Householder Symposium XVII, Zeuthen, Germany, June 16, 2008.
 Accurate algorithms for structured eigenvalue problems. Invited Talk in the Minisymposium Structured Matrix Algorithms: complexity and stability of the 6th International Congress on Industrial and Applied Mathematics (ICIAM07), UZHETH Zürich, Switzerland, July 1620, 2007.
 First order perturbation expansions for eigenvalues of singular matrix pencils. Invited Talk as ILAS Sponsored Lecturer at Workshop on Structured Perturbations, and Distance Problems in Matrix Computations, Bedlewo, Poznan, Poland, March 2630, 2007.
 A parametrization of the group of symplectic matrices and its applications. Talk in Joint GAMMSIAM Conference on Applied Linear Algebra, Düsseldorf, Germany. July 2427, 2006.
 Low rank perturbations of spectral canonical forms. Invited Talk at the Thematic Session Matrix Analysis and Applications of the International Congress on the Applications of Mathematics (ICAM 2006), Santiago de Chile, March 1317, 2006.
 Accurate Symmetric Rank Revealing and Eigen Decompositions of Structured Matrices. Talk in VI International Workshop on Accurate Solution of Eigenvalue Problems. Penn State University, University Park, Pennsylvania, USA. May 2225, 2006.
 Recent Results on Matrix Perturbation Theory. 4 hours long Minicourse at the Departament of Mathematics of Universidade do Minho (Braga, Portugal). Invited by Instituto de Matemáticas de la Universidade do Minho. September 39, 2005.
 Accurate symmetric rank revealing factorizations of some structured matrices. Talk in the Workshop on Numerical Linear Algebra in the conference Foundations of Computational Mathematics (FoCM 2005), University of Cantabria (Santander), Spain. 30 June9 July, 2005.
 On the distribution of rank in real symplectic matrices. Talk in GAMM Workshop on Applied and Numerical Linear Algebra with special emphasis on Linear Algebra in Systems and Control Theory, FernUniversität Hagen, Hagen, Germany. July 23, 2004.
 Perturbation theory of block LU factorization. Poster in V International Workshop on Accurate Solution of Eigenvalue Problems, FernUniversität Hagen, Hagen, Germany. June 28July 1, 2004.
 Series expansion of the LU and Cholesky factors of a matrix. Talk in SIAM Conference on Applied Linear Algebra, The College of William & Mary, Williamsburg, Virginia, USA, July 1519, 2003.
 An orthogonal high relative accuracy algorithm for the symmetric eigenproblem. Invited Talk in the Special Session Numerical Linear Algebra of the First Joint Meeting Real Sociedad Matemática EspañolaAmerican Mathematical Society. Sevilla, Spain, June 1821, 2003.
 Perturbation theory for simultaneous bases of singular subspaces and numerical applications. Invited Talk in International Workshop on Recent Trends in Numerical Linear Algebra, Leganés, June 1617, 2003.
 Computing accurate eigenvalues and eigenvectors of symmetric quasiCauchy matrices. Poster in IV International Workshop on Accurate Solution of Eigenvalue Problems, Split, Croatia, June 2427, 2002.
 Computing accurate eigenvalues and eigenvectors of symmetric quasiCauchy matrices. Talk in 2nd Conference on Applied Mathematics and Scientific Computing, Dubrovnik, Croatia, June 49, 2001.
 Perturbation theory for simultaneous bases of singular subspaces. Talk in III International Workshop on Accurate Solution of Eigenvalue Problems, FernUniversität Hagen, Germany. July 36, 2000.
Scientific Publications
Papers in journals indexed in Journal Citation Reports (JCR) of Web of Science (Thomson Reuters)
 L.M. Anguas, M.I. Bueno, and F.M. Dopico, Conditioning and backward errors of eigenvalues of homogeneous matrix polynomials under Möbius transformations, submitted (arXiv:1810.11495).
 F.M. Dopico and V. Noferini, Root polynomials and their role in the theory of matrix polynomials, submitted.
 F. De Terán, A. Dmytryshyn, and F.M. Dopico, Generic symmetric matrix pencils with bounded rank, submitted (arXiv:1808.03118).
 F.M. Dopico, S. Marcaida, and M.C. Quintana, Strong linearizations of rational matrices with polynomial part expressed in an orthogonal basis, submitted (arXiv:1806.10544).
 L.M. Anguas, M.I. Bueno, and F.M. Dopico, A comparison of eigenvalue condition numbers for matrix polynomials, submitted (arXiv:1804.09825).
 F.M. Dopico, J. Pérez, and P. Van Dooren, Block minimal bases lifications of matrix polynomials, Linear Algebra and its Applications, 562 (2019), pp. 163204 (arXiv:1803.06306).
 L.M. Anguas, F.M. Dopico, R. Hollister, and D.S. Mackey, Van Dooren's index sum theorem and rational matrices with prescribed structural data, submitted. Available as MIMS EPrint: 2018.6 of The University of Manchester.
 F.M. Dopico and P. Van Dooren, Robustness and perturbations of minimal bases II: The case with given row degrees, Linear Algebra and its Applications (2019) https://doi.org/10.1016/j.laa.2018.10.016 (arXiv:1712.03816).
 F. De Terán, F.M. Dopico, D.S. Mackey, and V. Perovic, Quadratic realizability of palindromic matrix polynomials, submitted. Available as MIMSeprint 2017.37 of The University of Manchester.
 M.I. Bueno, F.M. Dopico, S. Furtado, and L. Medina, A blocksymmetric linearization of odd degree matrix polynomials with optimal eigenvalue condition number and backward error, Calcolo, 55 (2018), 32:132:43.
 F.M. Dopico and J. GonzálezPizarro, A compact rational Krylov method for largescale rational eigenvalue problems, Numerical Linear Algebra with Applications (2018) DOI: 10.1002/nla.2214 (arXiv:1705.06982).
 A. Dmytryshyn and F.M. Dopico, Generic skewsymmetric matrix polynomials with fixed rank and fixed odd grade, Linear Algebra and its Applications, 536 (2018), pp. 118. (arXiv:1703.05797).
 F.M. Dopico, J. Pérez, and P. Van Dooren, Structured backward error analysys of linearized structured polynomial eigenvalue problems, Mathematics of Computation, (2018), https://doi.org/10.1090/mcom/3360 (arXiv:1612.07011v1).
 P. Van Dooren and F.M. Dopico, Robustness and perturbations of minimal bases, Linear Algebra and its Applications, 542 (2018), pp. 246281. (arXiv: 1612.03793).
 A. Dmytryshyn and F.M. Dopico, Generic complete eigestructures for sets of matrix polynomials with bounded rank and degree, Linear Algebra and its Applications, 535 (2017), pp. 213230. (arXiv: 1612.04085)
 M.I. Bueno, F.M. Dopico, J. Pérez, R. Saavedra, and B. Zykoski, A simplified approach to Fiedlerlike pencils via block minimal bases pencils, Linear Algebra and its Applications, 547 (2018), pp. 45104. (arXiv:1611.07170v1).
 A. Amparan, F.M. Dopico, S. Marcaida, and I. Zaballa, Strong linearizations of rational matrices, to appear in SIAM Journal on Matrix Analysis and Applications. Available as MIMSeprint 2016.51 of The University of Manchester.
 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. 80103. (arXiv:1606.02574)
 F.M. Dopico, P. Lawrence, J. Pérez, and P. Van Dooren, Block Kronecker linearizations of matrix polynomials and their backward errors, Numerische Mathematik, 140 (2018), pp. 373426. Extended version available as MIMSeprint 2016.34 of The University of Manchester.
 F.M. Dopico and K. Pomés, Structured condition numbers for linear systems with parameterized quasiseparable coefficient matrices, Numerical Algorithms, 73 (2016), pp. 11311158 (DOI 10.1007/s1107501601338).
 N. CastroGonzález, F.M. Dopico, and J.M. Molera, Multiplicative perturbation theory of the MoorePenrose inverse and the least squares problem, Linear Algebra and its Applications, 503 (2016), pp. 125.
 F. De Terán, F.M. Dopico, and J. Pérez, Eigenvalue condition numbers and pseudospectra of Fiedler matrices, Calcolo (2016). (DOI 10.1007/s1009201601899).
 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. 577597.
 F. De Terán and F. M. Dopico, Generic change of the partial multiplicities of regular matrix pencils under lowrank perturbations, SIAM Journal on Matrix Analysis and Applications, 37 (2016), pp. 823835.
 F. M. Dopico and K. Pomés, Structured eigenvalue condition numbers for parameterized quasiseparable matrices, Numerische Mathematik, 134 (2016), pp. 473–512 (DOI 10.1007/s0021101507795).
 F. De Terán, F. M. Dopico, and P. Van Dooren, Constructing strong lifications from dual minimal bases, Linear Algebra and its Applications, 495 (2016), pp. 344372.
 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. 460504.
 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.
 M. I. Bueno, F. M. Dopico, S. Furtado, and M. Rychnovsky, Large vector spaces of blocksymmetric strong linearizations of matrix polynomials, Linear Algebra and its Applications, 477 (2015), pp. 165210.
 F. M. Dopico, J. González, D. Kressner, and V. Simoncini, Projection methods for largescale TSylvester equations, Mathematics of Computation, 85 (2016), pp. 24272455.
 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. 302328.
 F. De Terán, F. M. Dopico, and J. Pérez, Backward stability of polynomial rootfinding using Fiedler companion matrices, IMA Journal of Numerical Analysis, 36 (2016), pp. 133173.
 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. 590622 .
 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. 13031328.
 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. 904930.
 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. 264333.
 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. 197230.
 F. M. Dopico, Alan Turing and the origins of modern Gaussian elimination, Arbor, Vol.189764 (2013), a084. dx.doi.org/10.3989/arbor.2013.764n6007.
 N. CastroGonz ález, J. Ceballos, F. M. Dopico, and J. M. Molera, Accurate solution of structured least squares problems via rankrevealing decompositions, SIAM Journal on Matrix Analysis and Applications, 34 (2013), pp. 11121128.
 F. De Terán, F. M. Dopico, and J. Pérez, Condition numbers for inversion of Fiedler companion matrices, Linear Algebra and its Applications, 439, 944981, (2013).
 F. De Terán, F. M. Dopico, and D. S. Mackey, Fiedler companion linearizations for rectangular matrix polynomials, Linear Algebra and its Applications, 437, 957991 (2012).
 C. Ferreira, B. Parlett, and F. M. Dopico, Sensitivity of eigenvalues of an unsymmetric tridiagonal matrix, Numerische Mathematik, 122 (2012), pp. 527555.
 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. 28172860.
 F. M. Dopico, V. Olshevsky, and P. Zhlobich, Stability of QRbased fast system solvers for a subclass of quasiseparable rank one matrices, Mathematics of Computation, 82 (2013), pp. 20072034.
 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. 849863.
 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. 448465.
 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. 463483.
 F. M. Dopico and J. M. Molera, Accurate solution of structured linear systems via rankrevealing decompositions, IMA Journal of Numerical Analysis, 32 (2012), pp.10961116 (doi:10.1093/imanum/drr023).
 F. M. Dopico and P. Koev, Perturbation theory for the LDU factorization and accurate computations for diagonally dominant matrices, Numerische Mathematik, 119 (2011), pp. 337371 (DOI: 10.1007/s0021101103823).
 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. 4467.
 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. 14641480. Also available as MIMS EPRINT 2010.33
 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. 21812204. Also available as MIMS EPRINT 2009.77.
 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. 892910.
 F.M. Dopico, P. Koev and J. M. Molera, Implicit standard Jacobi gives high relative accuracy, Numerische Mathematik, 113 (2009), pp. 519553.
 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. 371402.
 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. 650673.
 F. De Terán and F.M. Dopico, Low rank perturbation of regular matrix polynomials, Linear Algebra and its Applications, 430 (2009), pp.579586.
 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. 518531.
 F.M. Dopico y P. Koev, Bidiagonal decompositions of oscillating systems of vectors, Linear Algebra and its Applications, 428 (2008), pp. 25362548.
 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. 491496.
 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. 548576.
 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. 796813.
 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. 538547.
 P. Koev and F.M. Dopico, Accurate eigenvalues of certain sign regular matrices, Linear Algebra and its Applications, 424 (2007), pp. 435447.
 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. 496529.
 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. 567582.
 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. 2436.
 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. 11261156.
 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. 772778.
 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. 561581.
 M.I. Bueno and F.M. Dopico, Stability and sensitivity of tridiagonal LU factorization without pivoting, BIT, 44 (2004), pp. 651673.
 M.I. Bueno and F.M. Dopico, Stability and sensitivity of Darboux Transformation without parameter, Electronic Transactions on Numerical Analysis, 18 (2004), pp. 101136.
 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. 10211031.
 J. Moro and F.M. Dopico, Low rank perturbation of Jordan structure, SIAM Journal on Matrix Analysis and Applications, 25 (2003), pp. 495506.
 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. 301351.
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 F.M. Dopico, J. Moro and J.M. Molera, Weyltype relative perturbation bounds for eigensystems of Hermitian matrices, Linear Algebra and its Applications, 309 (2000), pp. 318.
 F.M. Dopico, A note on sin\Theta theorems for singular subspace variations, BIT,40 (2000), pp. 395403.
 S. H. Kwok, T.B. Norris, L.L. Bonilla, J. Galán, J.A. Cuesta, F. C. MartínezDopico, J.M. Molera, H.T. Grahn, K. Ploog, and R. Merlin, Domain wall kinetics and tunnelinginduced instabilities in superlattices, Physical Review B, 51 (1995), pp. 1017110174.
 F. C. MartínezDopico, J.A. Cuesta, J.M. Molera and R. Brito, Random versus deterministic twodimensional traffic flow models, Physical Review E, 51 (1995), pp. R835R838.
 J.M. Molera, F. C. MartínezDopico, J.A. Cuesta and R. Brito, Theoretical approach to twodimensional traffic flow models, Physical Review E, 51 (1995), pp. 175187.
 L.L. Bonilla, J. Galán, J.A. Cuesta, F. C. MartínezDopico 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. 86448657.
 J.A. Cuesta, F. C. MartínezDopico, J.M. Molera and A. Sánchez, Phase transitions in twodimensional traffic flow models, Physical Review E, 48 (1993), pp. R4175R4178.
 M. Soler, F. C. MartínezDopico and J.M. Donoso, Integral Kinetic Method for one dimension: The Spherical Case, Journal of Statistical Physics, 69 (1992), pp. 813835.
 F. C. MartínezDopico and M. Soler, An integral numerical method for a nonlinear FokkerPlanck equation, European Journal of Mechanics B/Fluids, 11 (1992), pp. 555572.