# Research Interests

## 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Items labelled by "u" are unpublished in peer reviewed journals (they may be currently under the refereeing process).See also my Google Scholar page.

7u. **Computing a compact local Smith form**, with P. Van Dooren. Preprint.

6u. **Invertible bases and root vectors for analytic matrix-valued functions**. Preprint.

5u. **The DL(P) vector space of pencils for singular matrix polynomials**, with F. Dopico. Preprint.

4u. **Eigenvalue avoidance of structured matrices depending
smoothly on a real parameter**, with Y. Nakatsukasa. Preprint.

3u. **Weighted enumeration of nonbacktracking walks on weighted graphs**, with F. Arrigo, D. J. Higham and R. Wood. Preprint.

2u. **Tropical Laurent series, their tropical roots, and localization results for the eigenvalues of nonlinear matrix functions**, with G. M. Negri-Porzio and L. Robol. Preprint.

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

45. **Perturbation theory of transfer function matrices**, with L. Nyman, J. Pérez and M. C. Quintana. Preprint. SIAM Journal on Matrix Analysis and Applications, To appear, 2023.

44. **On the Rellich eigendecomposition of para-Hermitian matrices and the sign characteristics of *-palindromic matrix polynomials**, with G. Barbarino. Preprint. Linear Algebra and its Applications, Vol. 672, pp. 1--27, 2023.

43. **Revisiting the matrix polynomial greatest common divisor**, with P. Van Dooren. Preprint. SIAM Journal on Matrix Analysis and Applications, To appear, 2023.

42. **When can forward stable algorithms be composed stably?**, with C. Beltrán and N. Vannieuwenhoven. Preprint. IMA Journal of Numerical Analysis, To appear, 2023.

41. **On computing root polynomials and minimal bases of matrix pencils**, with P. Van Dooren. Preprint. Linear Algebra and its Applications, Vol. 658, pp. 86--115, 2023.

40. **Root vectors of polynomial and rational matrices: theory and computation**, with P. Van Dooren. Preprint. Linear Algebra and its Applications, Vol. 656, pp. 510--540, 2023.

39. **On role extraction for digraphs via neighborhood pattern similarity**, with G. Barbarino and P. Van Dooren. Preprint. Physical Review E, Vol. 106, 054301, 2022.

38. **Dynamic Katz and related network measures**, with F. Arrigo, D. J. Higham and R. Wood. Preprint. Linear Algebra and its Applications, Vol. 655, pp. 159--185, 2022.

37. **Cyclically presented groups as Labelled Oriented Graph groups**, with G. Williams. Preprint. Journal of Algebra, Vol. 605, pp. 179--198, 2022.

36. **The limit empirical spectral distribution of Gaussian monic complex matrix polynomials**, with G. Barbarino. Preprint. Journal of Theoretical Probability, 2022, https://doi.org/10.1007/s10959-022-01163-3.

35. **The limit empirical spectral distribution of complex matrix polynomials**, with G. Barbarino. Preprint. Random Matrices: Theory and Applications, 2250023, 2021.

34. **Matrices in companion rings, Smith forms, and the homology of 3-dimensional Brieskorn manifolds**, with G. Williams. Preprint. Journal of Algebra, Vol. 587, pp. 1--19, 2021.

33. **Nearest Ω-stable matrix via Riemannian optimization**, with F. Poloni. Preprint. Numerische Mathematik, Vol. 148, pp. 817--851, 2021.

32. **A theory for backtrack-downweighted walks**, with F. Arrigo and D. J. Higham. Preprint. SIAM Journal on Matrix Analysis and Applications, Vol. 42, No.3, pp. 1229--1247, 2021.

31. **Structured backward errors in linearizations**, with L. Robol and R. Vandebril. Preprint. Electronic Transactions on Numerical Analysis, Vol. 54, pp. 420--442, 2021.

30. **Beyond non-backtracking: non-cycling centrality measures**, with F. Arrigo and D. J. Higham. Proceedings of the Royal Society A, Vol. 476:20190653, 2020.

29. **Wilkinson's bus: Weak condition numbers, with an application to singular polynomial eigenproblems**, with M. Lotz. Preprint. Foundations of Computational Mathematics, Vol. 20, pp. 1439--1473, 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-comrade and 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 **. Link. 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

7. V. Noferini and P. Van Dooren, **compactSmith**, a function to compute the ``compact" local Smith form. MATLAB implementation available via github . 2023.

5. V. Noferini and P. Van Dooren, **GCRDr**, a function to compute the compact greatest common right divisor of a pair of polynomial matrices having the same number of columns. MATLAB implementation available via github . 2022.

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.