Research

This is what I (should) do for a living now. I am a PhD student.

Presentations and talks

A selection of some of my conference talks.

• (pdf) 2009 Geometric means of more than two matrices SIAM Applied Linear Algebra Conference, Monterey, CA (USA); minisymposium on functions of matrices.
• (pdf) (italian) 2009 Medie, baricentri e matrici. Un problema tra il classico e il moderno.
  On the same topic as the preceeding one, but made for a divulgation talk for the Mathesis association, Bergamo (Italy).
• (pdf) 2008 Some implementation issues on the GKO algorithm. Structured Linear Algebra Problems: Analysis, Algorithms, and Applications, Cortona (Italy).
  Based on the paper A note on the O(n)-storage implementation of the GKO algorithm, see below.
• (pdf) 2007 Exploiting displacement structure in the solution of a class of nonsymmetric algebraic Riccati equations. 2nd international conference on matrix methods and operator equations, Moscow.
  Based on my master thesis work.

Papers

• (pdf) 2008 D. A. Bini, B. Meini, F. Poloni. An effective matrix geometric mean satisfying the Ando-Li-Mathias properties. Math. Comp. 79 (2010), pp. 437–452.
(pdf) 2008 D. A. Bini, B. Meini, F. Poloni. Fast solution of a certain Riccati equation through Cauchy-like matrices. ETNA} 33 (2009), pp. 84–104.
• (pdf) 2007 D. A. Bini, B. Iannazzo, F. Poloni. A fast Newton's method for a nonsymmetric algebraic Riccati equation. SIMAX 30 (2008), no. 1, pp. 276--290.

Pre-prints and e-prints

(excluding those relative to the papers listed above)
For the latest news, check my arXiv.org author page or subscribe to its atom feed.

• (pdf) 2009 F. Poloni. Constructing matrix geometric means. arXiv:0906.3132 [math.NA].
• (pdf) 2009 F. Poloni. A note on the O(n)-storage implementation of the GKO algorithm. arXiv:0903.4569v2 [math.NA].
• (pdf) 2008 D. A. Bini, B. Meini, F. Poloni. From algebraic Riccati equations to unilateral quadratic matrix equations: old and new algorithms. Submitted (Num. Math.)
• (pdf) 2008 D. A. Bini, B. Iannazzo, B. Meini, F. Poloni. Nonsymmetric algebraic Riccati equations associated with an M-matrix: recent advances and algorithms.In print (World Scientific Publishing)
• (pdf) 2006 D. A. Bini, F. Poloni. A note on the location of polynomial roots. arXiv:math/0609297v1 [math.NA].

Erdős number

Five (5), currently.

Exams

These are old projects I did while studying, as seminar exams, theses, or similar stuff. Published here because you might like them.

• (pdf) (italian) 2007 Metodi per la soluzione veloce di una classe di equazioni di Riccati algebriche, my master thesis.
• (pdf) (italian) 2006 Presentation on the complexity of matrix multiplication. Should be fun, but probably not easy to understand. They were meant as support slides for a presentation to be done mainly on the blackboard.
• (pdf) (italian) 2006 Short essay on the basis of classification using support vector machines. For an Operations Research exam.
• (tgz) 2006 A tool to cluster strings based on common words, using eigenvalue techniques. Probably impossible to use as it is nearly undocumented.
• (tgz) (italian) 2006 A small (command-line) phonebook program that supports searches using tries.
• (pdf) (italian) 2005 Fattorizzazione canonica e trasformata discreta di Fourier in un problema di teoria delle code, my bachelor thesis. Not much fun probably.
• (pdf) (italian) 2004 Problemi di partizione e copertura, (very) short essay for my Operations Research exam.
• (pdf) (italian) 2002 Una dimostrazione elementare dell'ellitticità delle orbite, small dissertation for my high school diploma. Sounds fun, at least to me.