Department of Mathematics
University of Pisa

 Numerical Analysis  and Computational Mathematics

Dario Andrea Bini
Research activity:
The common feature of the research activities is the development of mathematical tools for the design, analysis and implementation of algorithms for the efficient solution of computational problems. Particular interest is devoted to the analysis of structures, to their exploitation and to the complexity analysis of problems in both sequential and parallel model of computation. A special attention is addressed to numerical issues and to problems arising from applications.  Specific topics are


Papers  (1977-1989):

Papers  (1990-):

  1. Solving the generalized eigenvalue problem for rational Toeplitz matrices, SIAM J. Matrix Anal. Appl. 11, 1990 (with F. Di Benedetto).
  2. On the Euclidean scheme for polynomials having interlaced real zeros, Proceedings of 2-nd Annual ACM Symposium on Parallel Algorithms and Architectures, Crete, 1990, 254-258 (with L. Gemignani).
  3. A new preconditioner for the parallel solution of positive definite Toeplitz systems, Proceedings of 2-nd Annual ACM Symposium on Parallel Algorithms and Architectures, Crete, 1990, 220-223 (with F. Di  Benedetto).
  4. Parallel complexity of tridiagonal symmetric eigenvalue problem, Proc. 2-nd Ann. ACM-SIAM Symp.  on Discrete Algorithms, 384-393, 1990 (with V. Pan).
  5. Parallel polynomial computations by recursive processes, Proc. ACM SIGSAM Intern. Symp. on Symbolic and Algebraic Comp., 294, 1990 (with V. Pan).
  6. Improved parallel computations with matrices and polynomials, Proc. 18-th Intern. Symposium on Automata, Languages and Programming, Lectures Notes in Computer Science, 510, 520-531, Springer  1991 (with L. Gemignani and V. Pan).
  7. On the evaluation of the eigenvalues of a banded Toeplitz block matrix, J. of Complexity, 7, 408-424, 1991 (with V. Pan).
  8. Complexity of polynomial computations, in Complexity of Structured Computational Problems, Applied Mathematics Monographs, Comitato Nazionale per le Scienze Matematiche del CNR, Giardini, Pisa, 1991.
  9. An observation on certain spectral properties of Toeplitz matrices, Calcolo28, 37-43, 1991 (with F. Di Benedetto).
  10. Practical improvement of the divide-and-conquer eigenvalue algorithms, Computing48, 109-123, 1992 (with V. Pan).
  11. On the complexity of polynomial zeros, SIAM J. Comput. 21, 781-799 (1992) (with L. Gemignani).
  12. Divide and conquer techniques for the polynomial root-finding problem, Proc. World Congress of Nonlinear Analists, Tampa, Florida, August 1992, Walter de Gruyter, Berlin 1996.
  13. On a Matrix algebra related to the Hartley transform, SIAM J. Matrix Analysis Appl., 14,2, 500-507, 1993 (with P. Favati).
  14. Improved parallel polynomial division, SIAM J. Comput. 22,3, 617--626, 1993 (with V. Pan).
  15. Improved parallel computations with Toeplitz-like and Hankel-like matrices, Linear Algebra Appl., 188,189, 3--29, 1993 (with V. Pan).
  16. Fast discrete transform by means of eigenpolynomials, Computers & Mathematics (with Applications), 26,9, 35--52, 1993 (with E. Bozzo).
  17. Solving certain queueing problems modelled by Toeplitz matrices, Calcolo,30,4, 395--420, 1993 (with B. Meini).
  18. Iteration schemes for the divide-and-conquer eigenvalue solver, Numer. Math. 67, 403--425, 1994 (with L. Gemignani).
  19. Fast parallel computation of the polynomial remainder sequence via Bezout and Hankel matrices, SIAM J. Comput., 24,1, 63-77, 1995 (with L. Gemignani).
  20. A multiprecision implementation of a poly-algorithm for univariate polynomial zeros, Proc. of The POSSO Workshop on Software, Paris, 1995, J.C. Faug&egravere, J. Marchand, R. Rioboo editors (with G. Fiorentino).
  21. Adaptive Multiprecision Algorithm for Univariate Polynomial Zeros, Proc. of the First International MATHEMATICA Symposium, Computational Mechanics Publications, Southampton 1995, pp. 53--60 (with G. Fiorentino).
  22. 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 B. Meini)
  23. Numerical Computation of Polynomial Zeros by Means of Aberth's Method, Numerical Algorithms,  13, 1996 179-200.
  24. Graeffe's, Chebyshev, and Cardinal's processes for splitting a polynomial into factors, J. Complexity, 12, 492-511, 1996 (with V. Pan).
  25. On the solution of a nonlinear matrix equation arising in queueing problems. SIAM J. Matrix Anal. Appl. 17:906--926, 1996. (with B. Meini)
  26. Exploiting the Toeplitz structure in certain queueing problems. Calcolo, 33:289--305, 1996. (with B. Meini)
  27. Toeplitz matrices: structures, algorithms and applications. Calcolo, 33: 1--10, 1996. (with F. Di Benedetto)
  28. Improved cyclic reduction for solving queueing problems.  Numerical Algorithms, 15:57--74, 1997. (with B. Meini)
  29. MPSolve: 1.0: A Fortran 90 package for the numerical computation of polynomial roots, Dipartimento di Matematica Universita' di Pisa, 1997.(with V. Burchielli)
  30. 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 B. Meini)
  31. 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  B. Meini)
  32. Fast fraction-free triangularization of Bezoutians with applications to sub-resultant chain computation.  Linear Algebra Appl. , 284 (1998) 19-39 (with L. Gemignani).
  33. MPSolve: Numerical computation of polynomial roots v. 2.0, FRISCO report 1998 (with G. Fiorentino)
  34. Effective methods for solving banded Toeplitz systems, SIAM J. Matrix Anal. Appl., 20:700-719, 1999. (with B. Meini)
  35. 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 B. Meini).
  36. On the Parallel Evaluation of a Sparse Polynomial at a Point,  Numerical Algorithms, 20, pp. 323-329, 1999 (with G. Fiorentino)
  37. 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  B. Meini)
  38. 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 S. Chakravarthy and B. Meini).
  39. Design, Analysis and Implementation of a Multiprecision Polynomial Rootfinder, Numerical Algorithms 23 (2000) 127-173 (with G. Fiorentino).
  40. Using FFT-based techniques in polynomial and matrix computations: Recent advances and applications, Numer. Functional Analysis Optim., 21 (2000) pp. 47-66.
  41. 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. 57-72with S. Chakravarthy, B. Meini.
  42. 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 B. Meini, V. Ramaswami.
  43. 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 B. Meini)
  44. On the regularized solution of block banded block Toeplitz systems , in Proceedings of SPIE, Advanced Signal Processing Algorithms, Architectures, and Implementations IX, Vol. 4116, F. T. Luk Editor, pp. 135-146, 2000 (with A. Farusi, G. Fiorentino, B. Meini)
  45. Inversion of Circulant Matrices over $\Z_m$,    25th International Colloquium on Automata Languages and Programming (ICALP '98), Mathematics of Computations 70, 2001, pp. 1169-1182, (with G. M. Del Corso, G. Manzini, L. Margara).
  46. Factorization of analytic functions by means of Koenig's theorem and Toeplitz computations,   Numerische Math. 89 (2001) pp. 49--82 (with  B. Meini and L. Gemignani)
  47. Approximate displacement rank and applications, in Structured Matrices in Mathematics, Computer Science, and Engineering II,, V. Olshevsky Editor, Contemporary Mathematics 281, pp.215-232, American Mathematical Society, Rhode Island, 2001 (with B. Meini).
  48. 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, Nova Science Publisher Inc., New York, 2001, pp. 21-42 (with B. Meini).
  49. Computations with infinite Toeplitz matrices and polynomials, Linear Algebra Appl.343-344 (2002) pp. 21-61. (with L. Gemignani and B. Meini).
  50. Solving matrix polynomial equations arising in queueing problems, Linear Algebra Appl. 340 (2002), pp. 225-244. (with G. Latouche and B. Meini).
  51. Solving nonlinear matrix equations arising in tree-like stochastic processes, Linear Algebra Appl. To appear (with G. Latouche and B. Meini).
  52. Polynomial factorization through Toeplitz matrix computations, Linear Algebra Appl. To appear (with A. Boettcher).

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Books

  1. Introduzione Alla Matematica Computazionale, Zanichelli, Bologna 1987 (with  R. Bevilacqua, M. Capovani,  O. Menchi)
  2. Metodi Numerici per l'Algebra Lineare, Zanichelli, Bologna 1988 (with M. Capovani, O. Menchi).
  3. Metodi Numerici, Zanichelli, Bologna 1992 (with R. Bevilacqua, M. Capovani, O. Menchi)
  4. Polynomial and Matrix Computations, Vol 1: Fundamental Algorithms, Birkhauser, Boston 1994 (with V. Pan).
Software: