**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, Spain.

Teléfono: +34 91 624 9446

FAX: +34 91 624 9129

Despacho: 2.2.D.25 (Edificio Sabatini)

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.

- Strongly minimal linear polynomial system matrices of structured rational matrices. Invited talk in Special Session "Linear Algebra and Control Theory", 35th International Workshop on Operator Theory and its Applications (IWOTA24), Canterbury, United Kingdom, August 12-16, 2024.
- Riemannian optimization methods to compute the nearest singular pencil. Talk in "8th ALAMA Meeting, ALAMA 2024, Linear Algebra, Matrix Analysis and Applications", Gijón, Asturias, Spain, June 12-14, 2024.
- Beyond Rosenbrock's theorem. Invited talk in Minisymposium "Developments in Structured Matrices, On the occasion of Steve Mackey's 70th birthday", SIAM Conference on Applied Linear Algebra (LA24), Paris, France, May 13-17, 2024.
- Strongly minimal self-conjugate linearizations for polynomial and rational matrices. Invited talk in "DW75 (A Workshop on the occasion of the 75th Birthday of David S. Watkins)", Leuven, Belgium, May 9-10, 2024.
- Nearest singular pencil via Riemannian optimization. Invited talk in the conference "Computational and Applied Mathematics 2023" in honour of Marc Van Barel's retirement, Hotel Sierra Silvana, Selva di Fasano (Br), Italy, August 29-September 1, 2023.
- Backward stability in polynomial and rational eigenvalue problems solved via linearization. Plenary talk in the conference "Numerical Analysis and Scientific Computation with Applications (NASCA23)", Athens, Greece, July 3-6, 2023.
- Strongly minimal self-conjugate linearizations for polynomial and rational matrices. Invited talk in the Workshop on "Numerical Linear Algebra" in the conference "Foundations of Computational Mathematics 2023", Paris, France, June 12-21, 2023.
- Minimal rank factorizations of low rank polynomial matrices. Invited talk in Minisymposium "Bounded rank perturbations in matrix theory and related problems" in "25th Conference of the International Linear Algebra Society (ILAS 2023)", Madrid, Spain, June 12-16, 2023.
- Topological properties of bundles of matrix pencils under strict equivalence. Invited talk in Special Session "Matrices, Operators, Systems and Control. In honour of A.C.M. Ran" in "33rd International Workshop on Operator Theory and its Applications (IWOTA 2022)", Kraków, Poland, September 6-10, 2022.
- Linearizations of matrix polynomials via Rosenbrock polynomial system matrices. Invited talk in Minisymposium ''Companion Matrix Forms'' in ''24th Conference of the International Linear Algebra Society (ILAS 2022: Classical Connections)'', Galway, Ireland, June 20-24, 2022.
- Diagonal scalings for improving the accuracy of computed eigenvalues of arbitrary pencils. Invited talk in "Oselot (Online Seminar in Linear Algebra and Operator Theory)", April 21, 2022.
- Sets of matrix polynomials with bounded rank and degree and their generic eigenstructures. Invited talk in "Oselot" (Online Seminar in Linear Algebra and Operator Theory)", June 25, 2020.
- Beyond matrix eigenvalues. Colloquium. Department of Mathematics. Universidad Carlos III de Madrid, Leganés, Spain, January 30, 2020.
- Structural backward stability in rational eigenvalue problems solved via linearization. Invited talk in Minisymposium"Computing with rational functions" in "International Congress on Industrial and Applied Mathematics, ICIAM 2019", Valencia, Spain, July 15-19, 2019.
- Conditioning and backward errors of eigenvalues of homogeneous matrix polynomials under Möbius transformations. Invited talk in Minisymposium "Matrices over elementary divisors domains" in "22nd Conference of the International Linear Algebra Society (ILAS 2019: Linear Algebra without borders)", Río de Janeiro, Brazil, July 8-12, 2019.
- Polynomial, rational and nonlinear eigenvalue problems and their solution via linearizations. Plenary talk in "V Jornadas ALAMA: Numerical Linear Algebra", Universitat Politècnica de València, Valencia, Spain, June 17-18, 2019.
- Local linearizations of rational matrices with application to nonlinear eigenvalue problems. Plenary talk in The International Conference on Mathematical Modeling with Applications (M2A19), Rabat, Morocco, April 1-4, 2019.
- Sets of matrix polynomials with bounded rank and degree and their generic eigenstructures. Plenary talk in the "Workshop on Matrix Theory and beyond", Universidade de Lisboa, Lisboa, Portugal, December 14, 2018.
- Backward stability of polynomial and rational eigenvalue problems solved via linearizations. Plenary talk in "18th International Conference on Computational and Mathematical Methods in Science and Engineering" (2018 CMMSE), Rota, Cádiz, Spain, July 9-14, 2018.
- Van Dooren's index sum theorem and rational matrices with prescribed structural data. Talk in Meeting on "Linear Algebra, Matrix Analysis and Applications, ALAMA 2018", Universitat d'Alacant, Sant Joan d'Alacant, May 30-June 1, 2018.
- Solving different rational eigenvalue problems via different types of linearizations. Invited talk in Minisymposium "Nonlinear Eigenvalue Problems and Applications" in SIAM Conference on Applied Linear Algebra, Hong Kong Baptist University, Hong Kong, China, May 4-8, 2018.
- 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 4-8, 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 24-28, 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 17-20, 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 18-23, 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 22-25, 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 24-28, 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 11-15, 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, Louvain-la-Neuve, Belgium, July 8, 2016.
- Backward stability of polynomial root-finding using Fiedler companion matrices and pencils. Invited talk in "Seminario MATESCO" of Departamento de Matemáticas, Estadística y Computación de la Universidad de Cantabria. Facultad de Ciencias, Santander, Spain, November 16, 2015.
- Recent advances on inverse problems for matrix polynomials: the inverse row-degree 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 26-30, 2015.
- Structured linearizations that preserve the sign characteristic 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 10-14, 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 10-14, 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 6-10, 2015.
- Volker Mehrmann and modern factorizations of symplectic matrices. Talk in "Numerical Algebra, Matrix Theory, Differential-Algebraic Equations, and Control Theory", Conference in Honor of Volker Mehrmann on the occasion of his 60th birthday, Technische Universität Berlin, Germany. May 6-9, 2015.
- Backward stability of polynomial root-finding using Fiedler companion matrices. Invited Talk in International Conference on Structured Numerical Linear and Multilinear Algebra: Analysis, Algorithms and Applications. Kalamata (Greece). September 8-12, 2014
- Sylvester equations and the matrix symmetrizer problem. Invited Talk in "Minisymposium on Solution of Sylvester-like Equations and Canonical Forms" in 19th Conference of the International Linear Algebra Society, Sungkyunkwan University, Seul Campus, South Korea. August 6-9, 2014.
- Matrix polynomials with completely prescribed eigenstructure. Joint ALAMA-GAMM/ANLA 2014 Meeting, Universitat Politècnica de Catalunya, Barcelona, July 14-16, 2014.
- The inverse complex eigenvector problem for real tridiagonal matrices. Invited talk in Special session "Linear Algebra: Algorithms and Applications", First Joint International Meeting RSME-SCM-SEMA-SIMAI-UMI, Universidad del País Vasco, Bilbao, June 30-July 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 23-25, 2014.
- Highly accurate Numerical Linear Algebra. Invited plenary talk in XXIII CEDYA/XIII CMA (XXIII Congreso de Ecuaciones Diferenciales y Aplicaciones-XIII Congreso de Matemática Aplicada), Universitat Jaume I, Castelló de la Plana, Spain, September 9-13, 2013.
- Structured eigenvalue condition numbers for parameterized quasiseparable matrices. Talk in 18th Conference of the International Linear Algebra Society, Providence, RI, USA. June 3-7, 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 Applications-NLAA 2013, IIT Guwahati, Assam, India, January 15-18, 2013.
- Alan Turing and the origins of modern Gaussian elimination. Invited talk in International Symposium: The Alan Turing Legacy, Fundación Ramón Areces, Madrid, España, October 23-24, 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 Editor-in-Chief of LAA, University of Wisconsin, Madison, USA, October 10-14, 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, Belgium, September 10-14, 2012.
- Structured perturbation theory for diagonally dominant matrices. Talk in 3rd Meeting on Linear Algebra, Matrix Analysis, and Applications, ALAMA 2012, Leganés, Spain, June 27-29, 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 18-22, 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 SC2011-International Conference on Scientific Computing, S. Margherita di Pula, Sardinia, Italy. October 10-14, 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 Matemática Aplicada, Palma de Mallorca, Spain. September 5-9, 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 22-26, 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 18-22, 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 18-22, 2011.
- Structured perturbation theory of diagonally dominant matrices and numerical applications. Talk in Householder Symposium XVIII on Numerical Linear Algebra, Tahoe City, California. June 12-17, 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 21-25, 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 21-25, 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 2-4, 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 26-29, 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 26-29, 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 2-4, 2009.

- Doubly structured sets of symplectic matrices. Invited Talk at Conference on Structured Linear Algebra Problems: Analysis, Algorithms and Applications, Cortona, Italy, September 15-19, 2008.
- Implicit Jacobi algorithms for the symmetric eigenproblem. Invited Plenary Talk at 15th International Linear Algebra Society Conference, Cancún, México, June 16-20, 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 9-12, 2008.
- An orthogonal and symmetric high relative accuracy algorithm for the symmetric eigenproblem. Invited Plenary Talk at Householder Symposium XVII, Zeuthen, Germany, June 1-6, 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), UZH-ETH Zürich, Switzerland, July 16-20, 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 26-30, 2007.
- A parametrization of the group of symplectic matrices and its applications. Talk in Joint GAMM-SIAM Conference on Applied Linear Algebra, Düsseldorf, Germany. July 24-27, 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 13-17, 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 22-25, 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 3-9, 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 June-9 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 2-3, 2004.
- Perturbation theory of block LU factorization. Poster in V International Workshop on Accurate Solution of Eigenvalue Problems, FernUniversität Hagen, Hagen, Germany. June 28-July 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 15-19, 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 Española-American Mathematical Society. Sevilla, Spain, June 18-21, 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 16-17, 2003.
- Computing accurate eigenvalues and eigenvectors of symmetric quasi-Cauchy matrices. Poster in IV International Workshop on Accurate Solution of Eigenvalue Problems, Split, Croatia, June 24-27, 2002.
- Computing accurate eigenvalues and eigenvectors of symmetric quasi-Cauchy matrices. Talk in 2nd Conference on Applied Mathematics and Scientific Computing, Dubrovnik, Croatia, June 4-9, 2001.
- Perturbation theory for simultaneous bases of singular subspaces. Talk in III International Workshop on Accurate Solution of Eigenvalue Problems, FernUniversität Hagen, Germany. July 3-6, 2000.