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.

- Fast and backward stable computation of the eigenvalues of matrix polynomials,

Aurentz, J. L., Mach, T., Robol, L., Vandebril, R., Watkins, D. S., arXiv preprint arXiv:1611.10142, 2016. - Roots of Polynomials: on twisted QR methods for companion matrices and pencils,

Aurentz, J. L., Mach, T., Robol, L., Vandebril, R., Watkins, D. S., arXiv preprint arXiv:1611.02435, 2016. - Certified counting of roots of random univariate polynomials,

Cleveland, J., Dzugan, J., Hauenstein, J. D., Haywood, I., Mehta, D., Morse, A., Robol, L., Schlenk, T., 2014, arXiv preprint arXiv:1412.1771

### Papers

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

##### 2017

- Solvability and uniqueness criteria for generalized Sylvester-type equations

De Terán, F., Iannazzo, B., Poloni, F., and Robol, L., Linear Algebra and its Applications, 2017- DOI: 10.1016/j.laa.2017.07.010 - Fast Hessenberg reduction of some rank structured matrices,

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

- Efficient Ehrlich–Aberth iteration for finding intersections of interpolating polynomials and rational functions,

Robol, L., and Vandebril, R., Linear Algebra and its Applications, 2017 – DOI: 10.1016/j.laa.2017.05.010 - 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.

##### 2016

- Efficient cyclic reduction for Quasi-Birth-Death problems with rank structured blocks

Bini, D. A. and Massei, S. and Robol, L., Applied Numerical Mathematics, 2016 – 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.

##### < 2016

- A multiprecision algorithm for the solution of polynomials and polynomial eigenvalue problems,

Bini, D.A. and Robol, L. – Proceedings of the 2014 Symposium on Symbolic-Numeric Computation, 2014 – DOI: 10.1145/2631948.2631952. - 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.