You might be able to find more information on my Google Scholar profile.

Preprints

This section contains preprints that are currently submitted to a peer-reviewed journal and/or theses and other papers that are not published. Some notes that have not (yet?) submitted to journals can be on this list. Most of the following items are expected to migrate to the next section at some point in time.

  1. Fast solvers for 2D fractional diffusion equations using rank structured matrices
    Mazza, M., Massei, S., Robol L., arXiv preprint arXiv:1804.05522, 2018.
  2. Computing performability measures in Markov chains by means of matrix functions
    Masetti, G., Robol L., arXiv preprint arXiv:1803.06322, 2018.
  3. Finite element model updating for structural applications
    Girardi M., Padovani C., Pellegrini D., Porcelli M., Robol L., arXiv preprint arXiv:1801.09122, 2018.
  4. Low-rank updates and a divide-and-conquer method for linear matrix equations
    Kressner, D., Massei, S., and Robol, L., arXiv preprint arXiv:1712.04349, 2017.
  5. Nonsingular systems of generalized Sylvester equations: an algorithmic approach
    De Terán, F., Iannazzo, B., Poloni, F., and Robol, L., arXiv preprint arXiv:1709.03783, 2017.

Book(s)

  1. Core-Chasing Algorithms for the Eigenvalue problem
    Aurentz, J, L., Mach, T., Robol, L., Vandebril, R., Watkins, D. S, SIAM, Fundamentals of Algorithms series, July 2018.

Papers

The following papers, listed in reverse chronological order, are published (or accepted for publication) in a journal.

  1. Solving rank structured Sylvester and Lyapunov equations
    Massei, S., Palitta, D., and Robol, L., to appear in SIAM Journal on Matrix Analysis and Applications, 2018.
  2. Fast and backward stable computation of roots of polynomials, Part II: backward error analysis; companion matrix and companion pencil
    Aurentz, J. L., Mach, T., Robol, L., Vandebril, R., Watkins, D. S., SIAM Journal on Matrix Analysis and Applications, 2018 – DOI: 10.1137/17M1152802
  3. Factoring block Fiedler Companion Matrices
    Del Corso, G. M., Poloni, F., Robol, L., Vandebril, R., to appear in a volume of the Springer INdAM series, 2018.
  4. Quasi-Toeplitz matrix arithmetic: a MATLAB toolbox
    Bini, D. A., Massei, S., and Robol, L., to appear in Numerical Algorithms, 2018 – DOI: 10.1007/s11075-018-0571-6
  5. Fast and backward stable computation of the eigenvalues of matrix polynomials
    Aurentz, J. L., Mach, T., Robol, L., Vandebril, R., Watkins, D. S., to appear in Mathematics of Computation, 2018 – DOI: 10.1090/mcom/3338
  6. On quadratic matrix equations with infinite size coefficients encountered in QBD stochastic processes
    Bini, D. A., Massei, S., Meini, B., Robol, L., Numerical Linear Algebra with Applications, 2018 – DOI: 10.1002/nla.2128
  7. Solvability and uniqueness criteria for generalized Sylvester-type equations
    De Terán, F., Iannazzo, B., Poloni, F., and Robol, L., Linear Algebra and its Applications, 2018 –  DOI: 10.1016/j.laa.2017.07.010
  8. Efficient Ehrlich–Aberth iteration for finding intersections of interpolating polynomials and rational functions
    Robol, L., and Vandebril, R., Linear Algebra and its Applications, 2018 – DOI: 10.1016/j.laa.2017.05.010
  9. Fast Hessenberg reduction of some rank structured matrices
    Gemignani, L., Robol, L., SIAM Journal on Matrix Analysis and Applications, 2017 – DOI: 10.1137/16M1107851
  10. On the decay of the off-diagonal singular values in cyclic reduction
    Bini, D. A., Massei, S. and Robol, L., Linear Algebra and its Applications, 2017 – DOI: 10.1016/j.laa.2016.12.027
  11. Decay bounds for the numerical quasiseparable preservation in matrix functions
    Massei, S. and Robol, L., Linear Algebra and its Applications, 2017 – DOI: 10.1016/j.laa.2016.11.041
  12. A framework for structured linearizations of matrix polynomials in various bases
    Robol, L., Vandebril, R. and Van Dooren, P., SIAM Journal on Matrix Analysis and Applications, 2017 – DOI: 10.1137/16M106296X
  13. Efficient cyclic reduction for Quasi-Birth-Death problems with rank structured blocks
    Bini, D. A. and Massei, S. and Robol, L., Applied Numerical Mathematics, 2017 – DOI: 10.1016/j.apnum.2016.06.014.
  14. On a class of matrix pencils and ℓ-ifications equivalent to a given matrix polynomial,
    Bini, D. A. and Robol, L., Linear Algebra and Its Applications, 2016 – DOI: 10.1016/j.laa.2015.07.017.
  15. Quasiseparable Hessenberg reduction of real diagonal plus low rank matrices and applications,
    Bini, D. A. and Robol, L., Linear Algebra and Its Applications, 2016 – DOI: 10.1016/j.laa.2015.08.026.
  16. Solving secular and polynomial equations: A multiprecision algorithm,
    Bini, D. A. and Robol, L., Journal of Computational and Applied Mathematics, 2014 – DOI: 10.1016/j.cam.2013.04.037.

Theses

My PhD and master theses.

  1. Exploiting rank structures for the numerical treatment of matrix polynomials,
    Robol, L. My PhD thesis that I defended in November 2015, under the supervision of prof. Dario A. Bini, 2015.
  2. A rootfinding algorithm for polynomials and secular equations,
    Robol, L. – My master thesis on polynomial rootfinding at arbitrary precision, 2012.

Software

  • MPSolve is an open source package that approximates roots of polynomials with arbitrary precision. The package can solve polynomials represented in different basis as well as secular equations. News: MPSolve is also available on Android. You can check it out on the Play Store.