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. Rational Krylov for Stieltjes matrix functions: convergence and pole selection
    Massei S., R. L., arXiv preprint arXiv:1908.02032, 2019.
  2. Rational Krylov and ADI iteration for infinite size quasi-Toeplitz matrix equations
    R. L., arXiv preprint arXiv:1907.02753, 2019.
  3. Tensor methods for the computation of MTTA in large systems of loosely interconnected components
    Masetti G., R. L., arXiv preprint arXiv:1907.02449, 2019.
  4. Finite element model updating for structural applications
    Girardi M., Padovani C., Pellegrini D., Porcelli M., R. L., arXiv preprint arXiv:1801.09122, 2018.

Book(s)

  1. Core-Chasing Algorithms for the Eigenvalue problem
    Aurentz J, L., Mach T., R. 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. Computing performability measures in Markov chains by means of matrix functions
    Masetti G., R. L., to apper on Journal of Computational and Applied Mathematics, 2019.
  2. When is a matrix unitary or Hermitian plus low rank?
    Del Corso G., Poloni F., R. L., Vandebril R., to appear on Numerical Linear Algebra with Applications, 2019.
  3. Nonsingular systems of generalized Sylvester equations: an algorithmic approach
    De Terán F., Iannazzo B., Poloni F., and R. L., to appear on Numerical Linear Algebra with Applications, 2019.
  4. Fast solvers for 2D fractional diffusion equations using rank structured matrices
    Mazza M., Massei S., R. L., to appear in SIAM Journal on Scientific Computing, 2019.
  5. Low-rank updates and a divide-and-conquer method for linear matrix equations
    Kressner D., Massei S., and R. L., SIAM Journal on Scientific Computing, 41(2), 2019, DOI: 10.1137/17M1161038.
  6. Fast and backward stable computation of the eigenvalues of matrix polynomials
    Aurentz J. L., Mach T., R. L., Vandebril R., Watkins D. S., Mathematics of Computation, 2019 – DOI: 10.1090/mcom/3338
  7. Factoring block Fiedler Companion Matrices
    Del Corso G. M., Poloni F., R. L., Vandebril R., chapter in Structured Matrices in Numerical Linear Algebra: Analysis, Algorithms and Applications, Springer INdAM Series, 2019 – DOI: 10.1007/978-3-030-04088-8_7.
  8. Solving rank structured Sylvester and Lyapunov equations
    Massei S., Palitta D., and R. L., SIAM Journal on Matrix Analysis and Applications, 39(4), 2018 – DOI: 10.1137/17M1157155.
  9. Fast and backward stable computation of roots of polynomials, Part II: backward error analysis; companion matrix and companion pencil
    Aurentz J. L., Mach T., R. L., Vandebril R., Watkins D. S., SIAM Journal on Matrix Analysis and Applications, 2018 – DOI: 10.1137/17M1152802
  10. Quasi-Toeplitz matrix arithmetic: a MATLAB toolbox
    Bini D. A., Massei S., and R. L., to appear in Numerical Algorithms, 2018 – DOI: 10.1007/s11075-018-0571-6
  11. On quadratic matrix equations with infinite size coefficients encountered in QBD stochastic processes
    Bini D. A., Massei S., Meini B., R. L., Numerical Linear Algebra with Applications, 2018 – DOI: 10.1002/nla.2128
  12. Solvability and uniqueness criteria for generalized Sylvester-type equations
    De Terán F., Iannazzo B., Poloni F., and R. L., Linear Algebra and its Applications, 2018 –  DOI: 10.1016/j.laa.2017.07.010
  13. Efficient Ehrlich–Aberth iteration for finding intersections of interpolating polynomials and rational functions
    R. L., and Vandebril R., Linear Algebra and its Applications, 2018 – DOI: 10.1016/j.laa.2017.05.010
  14. Fast Hessenberg reduction of some rank structured matrices
    Gemignani L., R. L., SIAM Journal on Matrix Analysis and Applications, 2017 – DOI: 10.1137/16M1107851
  15. On the decay of the off-diagonal singular values in cyclic reduction
    Bini D. A., Massei S. and R. L., Linear Algebra and its Applications, 2017 – DOI: 10.1016/j.laa.2016.12.027
  16. Decay bounds for the numerical quasiseparable preservation in matrix functions
    Massei S. and R. L., Linear Algebra and its Applications, 2017 – DOI: 10.1016/j.laa.2016.11.041
  17. A framework for structured linearizations of matrix polynomials in various bases
    R. L., Vandebril R. and Van Dooren P., SIAM Journal on Matrix Analysis and Applications, 2017 – DOI: 10.1137/16M106296X
  18. Efficient cyclic reduction for Quasi-Birth-Death problems with rank structured blocks
    Bini D. A. and Massei S. and R. L., Applied Numerical Mathematics, 2017 – DOI: 10.1016/j.apnum.2016.06.014.
  19. On a class of matrix pencils and ℓ-ifications equivalent to a given matrix polynomial,
    Bini D. A. and R. L., Linear Algebra and Its Applications, 2016 – DOI: 10.1016/j.laa.2015.07.017.
  20. Quasiseparable Hessenberg reduction of real diagonal plus low rank matrices and applications,
    Bini D. A. and R. L., Linear Algebra and Its Applications, 2016 – DOI: 10.1016/j.laa.2015.08.026.
  21. Solving secular and polynomial equations: A multiprecision algorithm,
    Bini D. A. and R. 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.