Research Interests

  • Root-finding
  • Matrix Polynomials
  • Matrix Functions
  • Canonical Forms
  • Complex Network Analysis
  • Theory of numerical condition
  • Mathematical analysis of algorithm stability
  • Design of numerical algorithms
  • Applications of network analysis to science (e.g. biology, economics, finance)
  • Applications of matrix theory to pure mathematics (e.g. algebraic topology, group theory, number theory)
  • Publications

    Items labelled by "u" are unpublished in peer reviewed journals (they may be currently under the refereeing process).

    See also my Google Scholar page.

    5u. The limit empirical spectral distribution of Gaussian monic complexmatrix polynomials, with G. Barbarino. Preprint .

    4u. Nearest Ω-stable matrix via Riemannian optimization, with F. Poloni. Preprint .

    3u. Structured backward errors in linearizations, with L. Robol and R. Vandebril. Preprint .

    2u. Matrices in companion rings, Smith forms, and the homology of 3-dimensional Brieskorn manifolds, with G. Williams. Preprint .

    1u. On the Jordan form of the Fréchet derivative of a matrix function.

    30. Beyond non-backtracking: non-cycling centrality measures, with F. Arrigo and D. J. Higham. Proceedings of the Royal Society A, To appear, 2020.

    29. Wilkinson's bus: Weak condition numbers, with an application to singular polynomial eigenproblems, with M. Lotz. Preprint . Foundations of Computational Mathematics, To appear, 2020.

    28. Root polynomials and their role in the theory of matrix polynomials, with F. Dopico. Preprint . Linear Algebra and its Applications, Vol. 584, pp. 37-78, 2020.

    27. Non-backtracking PageRank, with F. Arrigo and D. J. Higham. Journal of Scientific Computing, Vol. 80, No.3, pp. 1419-1437, 2019.

    26. The structured condition number of a differentiable map between matrix manifolds, with applications, with B. Arslan and F. Tisseur. Preprint . SIAM Journal on Matrix Analysis and Applications, Vol. 40, No. 2, pp. 774-799, 2019.

    25. Inertia laws and localization of real eigenvalues for generalized indefinite eigenvalue problems , with Y. Nakatsukasa. Preprint . Linear Algebra and its Applications, Vol. 578, pp. 272-296, 2019.

    24. Non-backtracking alternating walks, with F. Arrigo and D. J. Higham. Preprint . SIAM Journal on Applied Mathematics, Vol. 79, No. 3, pp. 781-801, 2019.

    23. On the exponential generating function for non-backtracking walks, with F. Arrigo, P. Grindrod and D. J. Higham. Preprint . Linear Algebra and its Applications, Vol. 556, pp. 381-399, 2018.

    22. Nonbacktracking walk centrality for directed networks, with F. Arrigo, P. Grindrod and D. J. Higham. Preprint . Journal of Complex Networks, Vol. 6, No.1, pp. 54-78, 2018.

    21. The deformed graph Laplacian and its applications to network centrality analysis, with P. Grindrod and D. J. Higham. Preprint . SIAM Journal on Matrix Analysis and Applications, Vol. 39, No. 1, pp. 310-341, 2018.

    20. A formula for the Fréchet derivative of a generalized matrix function. Preprint. SIAM Journal on Matrix Analysis and Applications, Vol. 38, No.2, pp. 434-457, 2017.

    19. Vector spaces of linearizations of matrix polynomials: a bivariate polynomial approach, with Y. Nakatsukasa and A. Townsend. Preprint. SIAM Journal on Matrix Analysis and Applications, Vol. 38, No. 1, pp. 1-29, 2017.

    18. Chebyshev rootfinding via computing eigenvalues of colleague matrices: when is it stable?, with J. Pérez. Preprint. Mathematics of Computation, Vol. 86, No. 306, pp. 1741-1767, 2017.

    17. On the sign characteristics of Hermitian matrix polynomials, with V. Mehrmann, F.Tisseur, and H. Xu. Preprint. Linear Algebra and its Applications, Vol. 511, pp. 328-364, 2016.

    16. Fiedler-Chebyshev pencils, with J. Pérez. Preprint. SIAM Journal on Matrix Analysis and Applications, Vol. 37, No. 4, pp. 1600-1624, 2016.

    15. On the stability of computing polynomial roots via confederate linearizations, with Y. Nakatsukasa. Preprint. Mathematics of Computation, Vol. 85, No. 301, pp. 2391-2425, 2016.

    14. An algorithm to compute the polar decomposition of a 3x3 matrix, with N. J. Higham. Preprint. Numerical Algorithms, Vol. 73, No. 2, pp. 349-369, 2016.

    13. Numerical instability of resultant methods for multidimensional rootfinding, with A. Townsend. Preprint. SIAM Journal on Numerical Analysis, Vol. 54, No. 2, pp. 719-743, 2016.

    12. When is a Hamiltonian matrix the commutator of two skew-Hamiltonian matrices? Preprint. Linear and Multilinear Algebra, Vol. 63, No. 8, pp. 1531-1552, 2015.

    11. Duality of matrix pencils, Wong chains and linearizations, with F. Poloni. Preprint. Linear Algebra and its Applications, Vol. 471, pp 730-767, 2015.

    10. Tropical roots as approximations to eigenvalues of matrix polynomials, with M. Sharify and F. Tisseur. Preprint. SIAM Journal on Matrix Analysis and Applications, Vol. 36, No. 1, pp. 138-157, 2015.

    9. Computing the common zeros of two bivariate functions via Bézout resultants , with Y. Nakatsukasa and A. Townsend. Preprint. Numerische Mathematik, Vol. 129, No. 1, pp.181-209, 2015.

    8. Flanders' theorem for many matrices under commutativity assumptions, with F. De Terán, R. Lippert and Y. Nakatsukasa. Preprint. Linear Algebra and its Applications, Vol. 443, pp. 120-138, 2014.

    7. Locating the eigenvalues of matrix polynomials, with D. A. Bini and M. Sharify. Preprint. SIAM Journal on Matrix Analysis and Applications, Vol. 34, No. 4, pp. 1708-1727, 2013.

    6. Solving polynomial eigenvalue problems by means of the Ehrlich-Aberth method, with D. A. Bini. Preprint. Linear Algebra and its Applications, Vol. 439, No. 4, pp. 1130-1149, 2013.

    5. The Ehrlich-Aberth method for palindromic matrix polynomials represented in the Dickson basis, with L. Gemignani. Linear Algebra and its Applications, Vol. 438, No.4, pp. 1645-1666, 2013.

    4. Modifications of Newton's method for even-grade palindromic polynomials and other twined polynomials, with L. Gemignani. Numerical Algorithms, Vol. 61, No.2, pp. 315-329, 2012.

    3. The behaviour of the complete eigenstructure of a polynomial matrix under a generic rational transformation . Preprint. Electronic Journal of Linear Algebra, Vol. 23, pp. 607-624, 2012.

    2. The application of the Ehrlich-Aberth method to structured polynomial eigenvalue problems . PAMM, Vol. 11, No.1, pp. 919-922, 2011.

    1. Algebraic arctic curves in the domain-wall six-vertex model, with F. Colomo and A. G. Pronko. Preprint. Journal of Physics A: Mathematical and Theoretical, Vol. 44, No.19, 195201, 2011.

    Software

    5. V. Noferini and F. Poloni, nearest_real_eigenvalues, a function to compute the nearest matrix with all real eigenvalues. MATLAB implementation available via github . 2020.

    4. V. Noferini and F. Poloni, nearest_stable, two functions to compute the nearest (real or complex: available are different codes for each version) Hurwitz stable matrix. MATLAB implementation available via github . 2020.

    3. N. J. Higham and V. Noferini, polar_quaternion, a function to stably compute the polar decomposition of a 3x3 real matrix via quaternions. MATLAB implementation available via github . 2017.

    2. Y. Nakatsukasa, V. Noferini and A. Townsend, rootsb, a function to compute the common real zeros of two bivariate functions. Available in MATLAB Central File Exchange. 2013.

    1. Y. Nakatsukasa, V. Noferini and A. Townsend, chebfun2/roots, a function to compute the common real zeros of two bivariate functions. Available within the MATLAB package chebfun. 2013.

    Coauthors

    (includes papers in preparation not yet listed above)
    Francesca Arrigo Bahar Arslan Giovanni Barbarino Carlos Beltran
    Mario Berljafa Dario A. Bini Filippo Colomo Fernando De Terán V.
    Froilán M. Dopico Luca Gemignani Peter Grindrod Daniel Kressner
    Desmond J. Higham Nicholas J. Higham Ross Lippert Martin Lotz
    Stefano Massei Volker Mehrmann Yuji Nakatsukasa Javier Pérez A.
    Federico Poloni Andrei G. Pronko Leonardo Robol Meisam Sharify
    Françoise Tisseur Alex Townsend Raf Vandebril Nick Vannieuwenhoven
    Gerald Williams Hongguo Xu

    Conferences

    A few conferences I recently attended:

    SLA 2012, Leuven (Belgium)

    Chebfun and Beyond 2012, Oxford (UK)

    2GALN 2013, Rome (Italy)

    FUN13, Manchester (UK)

    ILAS 2013, Providence (USA)

    25th Biennial NA conference, Strathclyde (UK)

    CMA/CEDYA 2013, Castellon de la Plana (Spain)

    Structured Matrix Days 2014, Limoges (France)

    First FJIM, Bilbao (Spain)

    SLA 2014, Kalamata (Greece)

    VM60, Berlin (Germany)

    26th Biennial NA conference, Strathclyde (UK)

    ICIAM 2015, Beijing (China)

    Future conferences that I plan to attend:

    SIAM Conference on Applied Linear Algebra, Atlanta (USA)

    A nondecreasing integer sequence

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