### 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.

- When is a matrix unitary or Hermitian plus low rank?

Del Corso, G., Poloni, R., Robol L., Vandebril, R., arXiv preprint arXiv:1811.06854, 2018. - Computing performability measures in Markov chains by means of matrix functions

Masetti, G., Robol L., arXiv preprint arXiv:1803.06322, 2018. - Finite element model updating for structural applications

Girardi M., Padovani C., Pellegrini D., Porcelli M., Robol L., arXiv preprint arXiv:1801.09122, 2018.

### Book(s)

- 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.

- Nonsingular systems of generalized Sylvester equations: an algorithmic approach

De Terán, F., Iannazzo, B., Poloni, F., and Robol, L., to appear on Numerical Linear Algebra with Applictions, 2019. - Fast solvers for 2D fractional diffusion equations using rank structured matrices

Mazza, M., Massei, S., Robol L., to appear in SIAM Journal on Scientific Computing, 2019. - Low-rank updates and a divide-and-conquer method for linear matrix equations

Kressner, D., Massei, S., and Robol, L., SIAM Journal on Scientific Computing, 41(2), 2019, DOI: 10.1137/17M1161038. - Fast and backward stable computation of the eigenvalues of matrix polynomials

Aurentz, J. L., Mach, T., Robol, L., Vandebril, R., Watkins, D. S., Mathematics of Computation, 2019 – DOI: 10.1090/mcom/3338 - Factoring block Fiedler Companion Matrices

Del Corso, G. M., Poloni, F., Robol, 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. - Solving rank structured Sylvester and Lyapunov equations

Massei, S., Palitta, D., and Robol, L., SIAM Journal on Matrix Analysis and Applications, 39(4), 2018 – DOI: 10.1137/17M1157155. - 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 - 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 - 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 - 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 - 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 - Fast Hessenberg reduction of some rank structured matrices

Gemignani, L., Robol, L., SIAM Journal on Matrix Analysis and Applications, 2017 – DOI: 10.1137/16M1107851 - 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 - 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 - 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 - 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. - 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. - 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. - 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.

- 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. - 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.