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

the numerical solution of Markov chains and queueing problems,

Toeplitz and structured matrix computations,

polynomial computations.
Papers (19771989):
Papers (1990):

Solving the generalized eigenvalue problem for rational Toeplitz matrices,
SIAM
J. Matrix Anal. Appl. 11, 1990 (with F. Di Benedetto).

On the Euclidean scheme for polynomials having interlaced real zeros, Proceedings
of 2nd Annual ACM Symposium on Parallel Algorithms and Architectures,
Crete, 1990, 254258 (with L. Gemignani).

A new preconditioner for the parallel solution of positive definite Toeplitz
systems, Proceedings of 2nd Annual ACM Symposium on Parallel Algorithms
and Architectures, Crete, 1990, 220223 (with F. Di Benedetto).

Parallel complexity of tridiagonal symmetric eigenvalue problem, Proc.
2nd Ann. ACMSIAM Symp. on Discrete Algorithms, 384393, 1990
(with V. Pan).

Parallel polynomial computations by recursive processes, Proc. ACM SIGSAM
Intern. Symp. on Symbolic and Algebraic Comp., 294, 1990 (with V. Pan).

Improved parallel computations with matrices and polynomials, Proc.
18th Intern. Symposium on Automata, Languages and Programming, Lectures
Notes in Computer Science, 510, 520531, Springer 1991 (with
L. Gemignani and V. Pan).

On the evaluation of the eigenvalues of a banded Toeplitz block matrix,
J. of Complexity, 7, 408424, 1991 (with V. Pan).

Complexity of polynomial computations, in Complexity of Structured Computational
Problems, Applied Mathematics Monographs, Comitato Nazionale per
le Scienze Matematiche del CNR, Giardini, Pisa, 1991.

An observation on certain spectral properties of Toeplitz matrices, Calcolo28,
3743, 1991 (with F. Di Benedetto).

Practical improvement of the divideandconquer eigenvalue algorithms,
Computing48,
109123, 1992 (with V. Pan).

On the complexity of polynomial zeros, SIAM J. Comput. 21,
781799 (1992) (with L. Gemignani).

Divide and conquer techniques for the polynomial rootfinding problem,
Proc.
World Congress of Nonlinear Analists, Tampa, Florida, August 1992,
Walter de Gruyter, Berlin 1996.

On a Matrix algebra related to the Hartley transform, SIAM J. Matrix
Analysis Appl., 14,2, 500507, 1993 (with P. Favati).

Improved parallel polynomial division, SIAM J. Comput. 22,3,
617626, 1993 (with V. Pan).

Improved parallel computations with Toeplitzlike and Hankellike matrices,
Linear
Algebra Appl., 188,189, 329, 1993 (with V. Pan).

Fast discrete transform by means of eigenpolynomials, Computers &
Mathematics (with Applications), 26,9, 3552, 1993 (with E.
Bozzo).

Solving certain queueing problems modelled by Toeplitz matrices, Calcolo,30,4,
395420, 1993 (with B. Meini).

Iteration schemes for the divideandconquer eigenvalue solver, Numer.
Math. 67, 403425, 1994 (with L. Gemignani).

Fast parallel computation of the polynomial remainder sequence via Bezout
and Hankel matrices, SIAM J. Comput., 24,1, 6377, 1995 (with
L. Gemignani).

A multiprecision implementation of a polyalgorithm for univariate polynomial
zeros, Proc. of The POSSO Workshop on Software, Paris, 1995, J.C.
Faugère, J. Marchand, R. Rioboo editors (with G. Fiorentino).

Adaptive Multiprecision Algorithm for Univariate Polynomial Zeros, Proc.
of the First International MATHEMATICA Symposium, Computational Mechanics
Publications, Southampton 1995, pp. 5360 (with G. Fiorentino).

On cyclic reduction applied to a class of
Toeplitzlike matrices arising in queueing problems. In W.~J. Stewart,
editor, Computations with Markov Chains, pages 2138. Kluwer Academic
Publisher, Boston, 1995. (with B. Meini)

Numerical Computation of Polynomial Zeros by Means of Aberth's Method,
Numerical
Algorithms, 13, 1996 179200.

Graeffe's, Chebyshev, and Cardinal's processes for splitting a polynomial
into factors, J. Complexity, 12, 492511, 1996 (with V. Pan).

On the solution of a nonlinear matrix equation
arising in queueing problems. SIAM J. Matrix Anal. Appl. 17:906926,
1996. (with B. Meini)

Exploiting the Toeplitz structure in certain
queueing problems. Calcolo, 33:289305, 1996. (with
B. Meini)

Toeplitz matrices: structures, algorithms and applications. Calcolo,
33:
110, 1996. (with F. Di Benedetto)

Improved cyclic reduction for solving queueing
problems. Numerical Algorithms, 15:5774, 1997.
(with B. Meini)

MPSolve: 1.0: A Fortran 90 package for the
numerical computation of polynomial roots, Dipartimento di Matematica
Universita' di Pisa, 1997.(with V. Burchielli)

Inverting block Toeplitz matrices in block Hessenberg
form by means of displacement operators: application to queueing problems.Linear
Algebra Appl., 272:116, 1998. (with B. Meini)

Using displacement structure for solving
NonSkipFree 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 1737. (with B. Meini)

Fast fractionfree triangularization of Bezoutians with applications to
subresultant chain computation. Linear Algebra Appl. , 284
(1998) 1939 (with L. Gemignani).

MPSolve: Numerical computation of polynomial
roots v. 2.0, FRISCO report 1998
(with G. Fiorentino)

Effective methods for solving banded Toeplitz
systems, SIAM J. Matrix Anal. Appl., 20:700719, 1999.
(with B. Meini)

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. 211243, chapter 8 (with B. Meini).

On the Parallel Evaluation of a Sparse Polynomial at a Point,
Numerical Algorithms, 20, pp. 323329, 1999 (with G. Fiorentino)

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. 300311, Denver,
1999 (with B. Meini)

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. 247260,
B. Plateau, W.J. Stewart and M. Silva Editors, Prensas Unversitarias de
Zaragoza, Saragoza, Spain, Sept. 1999, (with S. Chakravarthy and B. Meini).

Design, Analysis and Implementation of a Multiprecision Polynomial
Rootfinder, Numerical Algorithms 23 (2000) 127173 (with
G. Fiorentino).

Using FFTbased techniques in polynomial and matrix computations: Recent
advances and applications, Numer. Functional Analysis Optim., 21 (2000)
pp. 4766.

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. 5772with S. Chakravarthy,
B. Meini.

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. 7386 with
B. Meini, V. Ramaswami.

Solving block banded block Toeplitz
systems with structured blocks: new algorithms and open problems, in
Proceedings of the 2nd workshop on largescale scientific computations,
Sozopol, Bulgaria, June 1999, M. Griebl, S. Margenov, P.Y. Yalamov eds.,
pp. 1524, 2000 (with B. Meini)

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. 135146, 2000
(with A. Farusi, G. Fiorentino, B. Meini)

Inversion of Circulant Matrices over $\Z_m$, 25th
International Colloquium on Automata Languages and Programming (ICALP
'98), Mathematics of Computations 70, 2001, pp. 11691182, (with G.
M. Del Corso, G. Manzini, L. Margara).

Factorization of analytic functions by means
of Koenig's theorem and Toeplitz computations, Numerische
Math. 89 (2001) pp. 4982 (with B. Meini and L. Gemignani)

Approximate displacement rank and applications,
in Structured Matrices in Mathematics, Computer Science, and
Engineering II,, V. Olshevsky Editor, Contemporary Mathematics
281, pp.215232, American Mathematical Society, Rhode Island, 2001
(with B. Meini).

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. 2142 (with B. Meini).

Computations with infinite Toeplitz matrices and polynomials,
Linear Algebra Appl.343344 (2002) pp. 2161.
(with L. Gemignani and B. Meini).

Solving matrix polynomial equations arising in queueing problems,
Linear Algebra Appl. 340 (2002), pp. 225244.
(with G. Latouche and B. Meini).

Solving nonlinear matrix equations arising in treelike stochastic
processes, Linear Algebra Appl. To appear (with G. Latouche and B. Meini).

Polynomial factorization through Toeplitz matrix computations,
Linear Algebra Appl. To appear (with A. Boettcher).
Books

Introduzione Alla Matematica Computazionale, Zanichelli, Bologna
1987 (with R. Bevilacqua, M. Capovani, O. Menchi)

Metodi Numerici per l'Algebra Lineare, Zanichelli, Bologna 1988
(with M. Capovani, O. Menchi).

Metodi Numerici, Zanichelli, Bologna 1992 (with R. Bevilacqua, M.
Capovani, O. Menchi)

Polynomial and Matrix Computations, Vol 1: Fundamental Algorithms,
Birkhauser, Boston 1994 (with V. Pan).
Software:

Markov Chains

Toeplitz Matrices

Polynomial Computations

Tridiagonal Eigenvalue Problem