Curriculum
Dario A. Bini
Born on January 2, 1950;
Laurea in Mathematics, University of Pisa 1973
Academic positions:
1990-: Full Professor of Numerical Analysis at the Department of Mathematics, University of Pisa.
1986-1990: Full Professor of Numerical Analysis at the Department of Mathematics, University of Rome "Tor Vergata"
1982-1986: Associate Professor at the Department of Mathematics, University of Pisa.
1978-1982: Assistant Professor at the Department of Mathematics, University of Pisa.
1975-1978: Researcher at the Department of Mathematics, University of Pisa.
1973-1974: Compulsory military service
Editorial work:
- Member of the Editorial Board of the journal Calcolo since 1998
- Associate Editor of the journal SIAM J. Matrix Analysis Appl. 2003--2014
- Associate Editor of Electronic Transactions on Numerical Analysis 2014-
- Associate Editor of the Electronic Journal of Linear Algebra 2016-
- Guest Editor of special issues of the journals Linear Algebra Appl., Calcolo, Stochastic Models, J. of Comp. Appl. Math.
- Editor of "The Georg Heinig Memorial Volume", Birkhauser 2010
Other activities:
Organization of several workshops and conferences among which:
-- "Toeplitz Matrices: Structures, Algorithms and Applications", Cortona(Italy) Sept. 1996
-- "Structured Matrices: Analysis, Algorithms and Applications", Cortona(Italy) Sept. 2000
-- "Structured Numerical Linear Algebra Problems: Algorithms and Applications", Cortona(Italy) Sept. 2004
-- "Structured Linear Algebra Problems: Analysis, Algorithms and Applications", Cortona(Italy) Sept. 2008
-- "Structured Matrix Analysis with Applications", special session within the AMS-UMI Joint Meeting, Pisa, June 2002
-- "Fifth International Conference on Matrix-Analytic Methods in Stochastic Models", Pisa, June 2005
-- 16th Conference of the International Linear Algebra Society (ILAS), Pisa, June 2010.
-- "Structured Numerical Linear and Multilinear Algebra Problems: Analysis, Algorithms, and Applications", Leuven, Sept. 2012
-- "Structured Numerical Linear and Multilinear Algebra: Analysis, Algorithms and Applications", Kalamata, Sept. 2014.
Member of the Board of Directors of ILAS, 2008-2012.
Member of the advisory board of ILAS 2014-
Selected plenary/invited lectures:
--The 19th ILAS conference, Seoul, August 2014,
--"Structured Matrices and Tensors: Analysis, Algorithms, and Applications", Taipei, Taiwan, Dec. 2014
--ICIAM, Budapest -minisymposium on structured matrices- 2011
--MOPNET: EPSRC Matrix and Operator Pencil Network, Edinburgh 2010
--The Third International Conference on Structured Matrices and Tensors, Hong-Kong 2010
--Haifa Matrix Theory Conference, May 2009
--Advanced Workshop on Trends and Developments in Linear Algebra, Trieste, July 2009
--Journees de l'ANR GECKO, Sophia Antipolis, Nov. 2007
--Haifa Matrix Theory Conference, April 2007
--ICIAM-07 -minisymp. on tensor analysis, Zurich, July 2007
--ICIAM-07 -minisymp. on structured matrices, Zurich, July 2007
--2nd International conference on matrix methods and operator equations, Moscow, July 2007
--13-th ILAS Conference, Amsterdam 2006
--The 2nd International Conference on Structured Matrices”, Hong Kong, 2006
Recent summer schools:
-- CIME Summer School "Exploiting Hidden Structure in Matrix Computations. Algorithms and Applications", Cetraro, June 2015
-- "Journées Nationales de Calcul Formel (JNCF) 2014" Luminy, Nov. 2014
-- "Advanced School and Workshop on Matrix Geometries and Applications", Trieste July 2013
Research projects:
In the framework of MIUR, PI of the national research projects PRIN 2002, PRIN 2004, PRIN 2006, PRIN 2008.
PI of several CNR and GNCS research projects.
Students and post-docs:
--Past Ph.D. Students: E.Bozzo, S.Serra Capizzano, G.Fiorentino, B.Meini, B.Iannazzo, P.Boito, F.Poloni, V.Noferini, L.Robol
--Past M.Sc. students: L.Gemignani, F.Di Benedetto
--Current Ph.D. Students: S.Massei
Books:
--D.A.Bini, B.Iannazzo, B.Meini, Numerical Solution of Algebraic Riccati Equations, SIAM Book Series Fundamentals of Algorithms, 2012
--D.A.Bini, G.Latouche, B.Meini, Numerical Methods for Structured Markov Chains, Oxford University Press, 2005
--D.Bini, V.Pan, Polynomial and Matrix Computations, Vol 1: Fundamental Algorithms, Birkhauser, Boston 1994.
--D.Bini, M.Capovani, G.Lotti, F.Romani, Complessità Numerica, Boringhieri 1981.
-- R.Bevilacqua, D.Bini, M.Capovani, O.Menchi, Introduzione Alla Matematica Computazionale, Zanichelli, Bologna 1987
--D.Bini, M.Capovani, O.Menchi, Metodi Numerici per l'Algebra Lineare, Zanichelli, Bologna 1988.
--R.Bevilacqua, D.Bini, M.Capovani, O.Menchi, Metodi Numerici, Zanichelli, Bologna 1992.
Software:
--Matlab files from the book: Numerical Solution of Algebraic Riccati Equations, SIAM 2012.
--SMCSolver, A Fortran 90 software tool, with a user friendly GUI, for solving Structured Markov Chains
--MPSolve v. 2.2, A package for computing polynomial zeros with arbitrarily large precision
--pzeros, A fortran77 package for computing polynomial zeros based on the Ehrlich-Aberth iteration
--Eigensolve v.1.1, Solving the tridiagonal eigenvalue problem by means of the Ehrlich-Aberth iteration
Bibliometrics (Nov. 2016):
MathSciNet: publications 120, citations 1152 from 681 authors, h-index 17
Scopus: publications 104, citations 1503, h-index 21
Google Scholar: citations 5154, h-index 38
ResearchGate: publications 186, citations 3387, h-index 31, RG score 34.05
Research Activity:
Field of interest: design and analysis of numerical algorithms for linear algebra and for polynomial computations, computational complexity.
The early papers of the 1980s concerned the complexity analysis of matrix multiplication. The concepts of "border rank" and of "approximate complexity" were introduced for the first time together with an algorithm for fast matrix multiplication leading to the exponent 2.779 of matrix multiplication complexity which improved Strassen's and Pan's algorithms. Border rank has become the key tool at the basis of the currently asymptotically fastest algorithms for computing matrix product.
Polynomial computations and their relationships with structured matrices, in particular Toeplitz matrices, is another research topic. The parallel complexity of polynomial division, the border rank of triangular Toeplitz matrices, the LU factorization of Bezout matrices and the Euclidean scheme have been part of the research subjects in this area. The joint book with V. Pan "Polynomial and Matrix Computations", Birkhauser 1998, is the synthesis of large part of the research carried out in this field.
Toeplitz matrices and their displacement structures have been the subject of part of the research with the analysis of Toeplitz preconditioners within matrix algebras like the tau class and the Hartley algebra.
Polynomial computations received a more concrete attention in terms of software design: the package MPSolve for computing zeros of polynomial with any precision, and its new release of 2014, is the most efficient fast and reliable tool for polynomial rootfinding since 2000.
More recently, interest has been addressed to computational problems, including linear systems and nonlinear matrix equations, encountered in solving certain queueing models where large (infinite) structured matrices appear. Here, an adaptation of the cyclic (CR )reduction algorithm to solve infinite block tridiagonal systems has been introduced and extended to infinite block Toeplitz-like systems in Hessenberg form. The same algorithm has been extended to the solution of matrix equations expressed by matrix polynomials and matrix Laurent series.
A novel interpretation of CR has been given in functional form in terms of the Graeffe iteration. Together with the use of canonical factorizations, this provided new convergence results for CR and the design of new methods for general matrix equations. Part of the results are synthesized in the book "Numerical methods for structured Markov chains", Oxford 2005, jointly written with G. Latouche and B. Meini.
Numerical methods for algebraic Riccati equations (AREs) is another area of interest. New doubling algorithms for AREs have been introduced in particular a method for the transport equation. The book "Numerical Solution of Algebraic Riccati Equations", SIAM 2012, joint with B. Iannazzo and B. Meini, contains the state of the art of the research on algebraic Riccati equations.
A topic of interest concerns the analysis of rank structured matrices like the semiseparable and quasiseparable classes. Algorithms for performing the QR iterations with a low complexity per step have been designed and applied to companion-like matrices. In this framework, linearizations and l-ifications of matrix polynomials hav been introduced togeter with localizations of the roots of matrix polynomials.
Part of the research concerns the interplay between symbolic and numeric tools in certain polynomial computations involving structured matrices and CAGD, where results having both theoretical and algorithmic interest have been obtained.
Another subject concerns the definition of the concept of geometric mean of positive definite matrices with the design and analysis of algorithms for its computations. Recent results have been obtained, particular attention has been addressed to the solution of a related matrix equation involving the matrix logarithm.