Department of Mathematics
University of Pisa

 Numerical Analysis  and Computational Mathematics

1. Solving certain queueing problems modelled by Toeplitz matrices. Calcolo, 30:395--420, 1993. (with D. Bini)
2. On the solution of a nonlinear matrix equation arising in queueing problems. SIAM J. Matrix Anal. Appl. 17:906--926, 1996. (with D. Bini)
3. Exploiting the Toeplitz structure in certain queueing problems. Calcolo, 33:289--305, 1996. (with D. Bini)
4. Performance evaluation of a worst case model of the MetaRing MAC protocol with global fairness. Performance Evaluation, 29:127--151, 1997. (with G. Anastasi e L. Lenzini)
5. An improved  FFT-based version of Ramaswami's formula. Comm. Statist. Stochastic Models, 13:223-238, 1997.
6. Improved cyclic reduction for solving queueing problems.  Numerical Algorithms, 15:57--74, 1997. (with D. Bini)
7. New convergence results on functional iteration techniques for the numerical solution of M/G/1 type Markov chains. Numerische Mathematik, 78:39--58, 1997.
8. Solving M/G/1 type Markov chains: recent advances and applications. Comm. Statist. Stochastic Models, 14: 479-496, 1998.
9. Inverting block Toeplitz matrices in block Hessenberg form by means of displacement operators: application to queueing problems.Linear Algebra Appl., 272:1-16, 1998. (with D. Bini)
10. An efficient numerical method for performance analysis of contention MAC protocols: a case study (PRMA++). IEEE Journal on Selected Areas in Communications, 16:653-667, 1998. (with L. Lenzini, E. Mingozzi.)
11. Relaxed functional iteration techniques for the numerical solution of M/G/1 type Markov chains. BIT Numerical Mathematics, 38:510-526, 1998 (with P. Favati).
12. Solving QBD problems: the cyclic reduction algorithm versus the invariant subspace method. Advances in Performance Analysis, 1:215-225, 1998.
13. On functional iteration methods for solving nonlinear matrix equations arising in queueing problems,  IMA Journal of Numerical Analysis, 19:39-49, 1999 (with P. Favati).
14. Effective methods for solving banded Toeplitz systems, SIAM J. Matrix Anal. Appl., 20:700-719, 1999. (with D. Bini)
15. Solving certain queueing problems by means of regular splittings, Appl. Math. Letters, 13:99-105, 2000 (with P. Favati).
16. Factorization of analytic functions by means of Koenig's theorem and Toeplitz computations, Numerische Mathematik, 89:49-82, 2001. (with D. Bini and L. Gemignani).
17. Approximate displacement rank and applications, in Structured Matrices in Operator Theory, Numerical Analysis, Control, Signal and Image Processing, Contemporary Mathematics, vol. 281, V. Olshevsky Editor, pages 215-232, Amer. Math. Soc., Providence, RI, 2001. (with D. Bini).
18. Efficient computation of the extreme solutions of $X+A^* X^{-1}A=Q$ and $X-A^*X^{-1}A=Q$, Mathematics of Computations, 239:1189-1204, 2002.
19. Computations with infinite Toeplitz matrices and polynomials, Linear Algebra Appl., 343/344:21-61 (2002), (with D. A. Bini and L. Gemignani).
20. A shifted cyclic reduction algorithm for QBDs, SIAM J. Matrix Anal. Appl.,23:673-691, 2001/02 (with C. He and N. Rhee).
21. Solving matrix polynomial equations arising in queueing problems, Linear Algebra Appl., 340:225-244, 2002 (with D. A. Bini and G. Latouche).
22. Solving nonlinear matrix equations arising in Tree-Like stochastic processes, , Linear Algebra Appl., 366:39-64, 2002 (with D. A. Bini and G. Latouche).
23. Solving certain matrix equations by means of Toeplitz computations: algorithms and applications. Contemporary Mathematics, vol. 323, 151--167, Amer. Math. Soc., Providence, RI, 2003 (with D. A. Bini and L. Gemignani).
24. Effective fast algorithms for polynomial spectral factorization , Numerical Algorithms, 34:217-228, 2003  (with D.A. Bini, G. Fiorentino and L. Gemignani).
    
25. A quadratically convergent Bernoulli-like algorithm for solving matrix polynomial equations in Markov chains,  Electronic Transactions on Numerical Analysis (ETNA), 17:151-167, 2004. (with C. He, N. Rhee, K. Sohraby).
    
26. Non-Skip-Free M/G/1-type Markov  chains and Laurent matrix power series,  Linear Algebra Appl., 386:187-206, 2004 (with D.A. Bini).
    
27. The matrix square root from a new functional perspective: theoretical results and computational issues, SIAM J. Matrix Anal. Appl., 26:362-376, 2004/05
28. Algorithms for the Matrix p'th Root, Numerical Algorithms,  39 (2005), no. 4, 349--378 (with D.A. Bini and N.J. Higham).
    
29. Shift techniques and canonical factorizations in the solution of M/G/1-type Markov chains, Stochastic Models,  21 (2005), no. 2-3, 279--302 (with D.A. Bini and I. M. Spitkovsky).
30. On the solution of Riccati equations arising in fluid queues, Linear Algebra Appl. 413 (2006), no. 2-3, 474-494 (with D.A. Bini, B. Iannazzo and G. Latouche).
31. Nonlinear matrix equations and structured linear algebra, Linear Algebra Appl. 413 (2006), no. 2-3, 440-457.
32. On the doubling algorithm for a (shifted) nonsymmetric algebraic Riccati equation . SIAM J. Matrix Anal. Appl., 29 (2007), no. 4, 1083-1100 (with G.H. Guo and B. Iannazzo)
33. A probabilistic interpretation of cyclic reduction and its relationships with logarithmic reduction . Calcolo , 45 (2008), no. 3, 207-216 (with D.A. Bini and V. Ramaswami)
34. Fast solution of a certain Riccati equation through Cauchy-like matrices . Electron. Trans. Numer. Anal , 33 (2008/09), 84--104 (with D.A. Bini and F. Poloni)
35. The cyclic reduction algorithm: from Poisson equation to stochastic processes and beyond. In memoriam of Gene H. Golub . Numer. Algorithms , 51 (2009), no. 1, 23--60 (with D.A. Bini)
36. A note on computing the tail decay of M/G/1-type Markov renewal processes . Stoch. Models , 25 (2009), no. 4, 569--579 (with D.A. Bini and V. Ramaswami)
37. An effective matrix geometric mean satisfying the Ando-Li-Mathias properties . Math. Comp. , 79 (2010), no. 269, 437--452. (with D.A. Bini and F. Poloni)

1. On cyclic reduction applied to a class of Toeplitz-like matrices arising in queueing problems. In W. J. Stewart, editor, Computations with Markov Chains, pages 21--38. Kluwer Academic Publisher, Boston, 1995. (with D. Bini)
2. Using displacement structure for solving Non-Skip-Free M/G/1 type Markov chains. In Advances in Matrix Analytic Methods for Stochastic Models - Proceedings of the 2nd international conference on matrix analytic methods, A. Alfa and S. Chakravarthy Eds., 1998, Notable Publications Inc, NJ, pages 17-37. (with D. Bini)
3. On functional iteration methods for solving M/G/1 type Markov chains. In Advances in Matrix Analytic Methods for Stochastic Models - Proceedings of the 2nd international conference on matrix analytic methods, A. Alfa and S. Chakravarthy Eds., 1998, Notable Publications Inc, NJ, pages 44-54 (with P. Favati).
4. A New Algorithm for the Design of Capacity Service Units, in Proceedings of the Third international Conference on the Numerical Solution of Markov Chains, pp. 247-260, B. Plateau, W.J. Stewart and M. Silva Editors, Prensas Unversitarias de Zaragoza, Saragoza, Spain, Sept. 1999. (with D. Bini and S. Chakravarthy)
5. Solving block banded block Toeplitz systems with banded Toeplitz blocks, in Advanced Signal Processing Algorithms, Architectures, and Implementations IX, F.T. Luk Editor, Proceedings of SPIE, vol 3807, pp. 300-311, Denver, 1999 (with D.A. Bini).
6. Fast algorithms for structured problems with applications to Markov chains and queueing models,  in Fast Reliable Methods for Matrices with Structure,  T. Kailath and A. Sayed Editors, SIAM Philadelphia 1999, pp. 211-243, chapter 8 (with D. Bini).
7. Solving block banded block Toeplitz systems with structured blocks: new algorithms and open problems, In Proceedings of the 2nd workshop on large-scale scientific computations, Sozopol, Bulgaria, June 1999, M. Griebl, S. Margenov, P.Y. Yalamov eds., pp. 15-24, 2000 (with D.A. Bini).
8. Control of the BMAP/PH/1/K queue with group services, in Advances in Algorithmic Methods for Stochastic Models, Proceedings of the Third Conference on Matrix Analytic Methods, G. Latouche and P. Taylor eds., Notable Publications, 2000, pp. 57-72 (with D.A. Bini and S. Chakravarthy).
9. Analyzing M/G/1 paradigms through QBDs: the role of the block structure in computing the matrix G, in Advances in Algorithmic Methods for Stochastic Models, Proceedings of the Third Conference on Matrix Analytic Methods, G. Latouche and P. Taylor eds., Notable Publications, 2000, pp. 73-86 (with D. A. Bini, V. Ramaswami).
10. On the regularized solution of block banded block Toeplitz systems, Proceedings of SPIE, Advanced Signal Processing Algorithms, Architectures, and Implementations IX, Vol. 4116, F. T. Luk Editor, pp. 135-146, 2000 (with D. A. Bini, A. Farusi and G. Fiorentino).
11. Matrix equations and structures: efficient solution of special discrete algebraic Riccati equations, Proceedings of the WLSSC00, Bulgaria, 2000, pages 578-585, L. Vulkov, J. Wasniewski and P. Yalamov editors, Springer, 2001.
    
12. Solving Block banded block Toeplitz systems with structured blocks: algorithms and applications, in Structured Matrices: Recent Developments in Theory and Computation, D.A. Bini, E. Tyrtyshnikov and P. Yalamov Editors, pages 21-42, Nova Science Publisher Inc., New York, 2001 (with D.A. Bini)
13. Modeling and Performance Evaluation of GPRS, Proceedings, IEEE VTC 2001, Rhodes, Greece, May 2001, pages 2108-2112 (with C. H. Foh, B. Wydrowski and M. Zukerman)
14. Distributions of reward functions on continuous-time Markov chains, Matrix-analytic methods (Adelaide, 2002), 39--62, G. Latouche and P. Taylor eds. World Sci. Publishing, River Edge, NJ, 2002. (with M. Bladt, M.F. Neuts and B. Sericola).
15. L. Lenzini, B. Meini, E. Mingozzi, G. Stea, An M/G/1 Queuing System with Multiple Vacations to Assess the Performance of a Simplified Deficit Round Robin Model, Proc. "Tools for Performance Evaluation", vol. 1, pp. 134-151, Urbana (USA), September 2003.
16. D. Bini, B. Meini, S. Steffe', B. Van Houdt, Structured Markov chains solver: algorithms, Proceedings of "Valuetools", ACM, Pisa (Italy), October 2006.
17. D. Bini, B. Meini, S. Steffe', B. Van Houdt, Structured Markov chains solver: software tools, Proceedings of "Valuetools", ACM, Pisa (Italy), October 2006.
18. From algebraic Riccati equations to unilateral quadratic matrix equations: old and new algorithms . Dagstuhl Seminar Proceedings 07461, Numerical Methods for Structured Markov Chains, Dagstuhl Seminar 07461, 11.11. - 14.11.2007, 2008, ISSN 1862 - 4405 (with Dario Bini and Federico Poloni)
19. Nonsymmetric algebraic Riccati equations associated with an M-matrix: recent advances and algorithms . Dagstuhl Seminar Proceedings 07461, Numerical Methods for Structured Markov Chains, Dagstuhl Seminar 07461, 11.11. - 14.11.2007, 2008, ISSN 1862 - 4405 (with Dario Bini, Bruno Iannazzo and Federico Poloni)
20. On the tail decay of M/G/1-type Markov renewal processes . Dagstuhl Seminar Proceedings 07461, Numerical Methods for Structured Markov Chains, Dagstuhl Seminar 07461, 11.11. - 14.11.2007, 2008, ISSN 1862 - 4405 (with Dario Bini and V. Ramaswami)
21. Structured Markov chains solver: tool extension . SMCTOOLS 2009, Pisa. (with D. Bini, S. Steffe' and B. Van Houdt)
22. Nonsymmetric algebraic Riccati equations associated with an M-matrix: recent advances and algorithms . in "Matrix methods: theory, algorithms, applications", V. Olshevsky and E. Tyrtyshnikov eds., World Scientific, ISBN: 978-981-283-601-4, 2010 (with D. Bini, B. Iannazzo and F. Poloni)

1. A Perron iteration for the solution of a quadratic vector equation arising in Markovian Binary Trees . arXiv:1006.0577v1 [math.NA], 2010 (with F. Poloni)

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