Analisi di strutture di matrici: metodi numerici e applicazioni

Structured matrix analysis: numerical methods and applications

COFIN 02: 2002-2004


PRIN 04: 2004-2006



Available Software


MPSolve Multi-precision Polynomial Rootfinder. Approximation to the roots of a polynomial to any required precision. Reference: D.A. Bini, G. Fiorentino, Design, Analysis, and Implementation of a Multiprecision Polynomial Rootfinder, Numer. Algo., 23 (2000) 127-173.

Polzeros Fortran77 program for computing the roots of a polynomial by means of simultaneous iterations. Reference: D. A. Bini, Numerical Computation of Polynomial Zeros by Means of Aberth's Method, Numer. Algo., 13 (1996), 179-200,

Polzeros Fortran90 implementation of Polzeros provided by Alan Miller CSIRO Mathematical & Information Sciences, Private Bag 10, Clayton South MDC, Victoria, Australia 3169. Alan.Miller@mel.dms.csiro.au, http://www.mel.dms.csiro.au/~alan.

SMCSolver Structured Markov Chains Solver in Fortran 95 with a graphical interface. Implementation of the most advanced algorithm for the solution of structured Markov chains including QBD, M/G/1, G/M/1, Non-Skip-Free.

SMCSolver Structured Markov Chains Solver Matlab Version, by Benny Van Houdt.

Eigensolve Fortran 95 module for computing generalized eigenvalues of tridiagonal matrices. Reference: D.A. Bini, L. Gemignani, F. Tisseur, The Ehrlich-Aberth Method for the Nonsymmetric Tridiagonal Eigenvalue Problem. SIAM J. Matrix Analysis Appl. vol. 27, pp. 153-175, 2005

IPSolve Fortran 95 Module for computing roots of polynomials by means of the inverse power method applied to a diagonal plus rank-one matrix. reference: D.A. Bini, L. Gemignani, V. Pan, Inverse power and Durand-Kerner iterations for univariate polynomial root-finding. Comput. Math. Appl. 47 (2004), no. 2-3, 447--459.

Set of test matrices

PCI Parametric Curve Intersection Fortran 95 module for computing the intersection of parametric curves by means of simultaneous iterations. Reference: D.A. Bini and A. Marco, "Computing curve intersection by means of simultaneous iterations", Numer. Algo. vol. 43, pp. 151-175, 2006.

toms729gw Fast solver for Toeplitz linear systems. Authors: A. Aricò and G. Rodriguez (for the Matlab MEX gateway). Authors: P.C. Hansen and T. Chan (for the computational routines). This is a Matlab (Fortran) MEX gateway for TOMS Algorithm 729, by P.C Hansen and T. Chan, which implements a look-ahead Levinson method for the solution of Toeplitz linear systems. The algorithm is described in the paper P.C. Hansen and T. Chan, FORTRAN subroutines for general Toeplitz systems ACM Transactions on Mathematical Software (TOMS), 18(3):256-273, 1992.
Last updated: November 21, 2007.

tpls Fast least squares solver for Toeplitz linear systems. Author: G. Rodriguez. This Matlab functions compute the least squares solution of an overdetermined, full-rank, Toeplitz linear system, by a fast algorithm. The method is based on the computation of the Schur complement of an augmented matrix, and is described in the paper G. Rodriguez, Fast solution of Toeplitz- and Cauchy-like least squares problems. SIAM J. Matr. Anal. Appl., 28(3):724-748, 2006.
Last updated: August 4, 2007.

corner.m: Find the corner of a discrete L-curve. Authors: P.C. Hansen, T.K. Jensen, and G. Rodriguez. This Matlab function implements an adaptive algorithm for computing the corner of a discrete L-curve. The L-curve is a technique used in regularization methods for estimating the regularization parameter. The algorithm is described in the paper P.C. Hansen, T.K. Jensen, and G. Rodriguez. An adaptive pruning algorithm for the discrete L-curve criterion. Journal of Computational and Applied Mathematics, 198(2):483-492, 2006.
This function has been included in Version 4 of the Regularization Tools by P.C. Hansen.
Last updated: January 11, 2007.

SMT Structured matrices toolbox. Authors: M. Redivo-Zaglia and G. Rodriguez. SMT is a Matlab toolbox for structured matrix computation. It is currently under development.
Last updated: July 15, 2006.

hess.cpp Efficient and stable solution of Hessenberg linear systems:

hesseigstru.m , giv.m , norm1est.m , matrixex.m A Unitary Hessenberg QR-based algorithm via semiseparable matrices:

compqr.m Fast QR iteration for companion matrices:

Antireflective boundary conditions Pacchetti di funzioni matlab per svolgere operazioni con l'algebra delle matrici generate da condizioni anti-riflettenti. Tale codice estende il toolbox "RestoreTools" (http://www.mathcs.emory.edu/~nagy/RestoreTools) con le CC anti-riflettenti per il prodotto matrice-vettore e quindi per tutti i metodi iterativi regolarizzanti (CGLS, PCGLS, etc.). E' disponibile un codice per risolvere in modo ``fast'' il sistema lineare derivante da condizioni al contorno anti-riflettenti e PSF fortemente simmetrica (utilizza la DST).

Software per ricostruzioni SPECT Software prototipale in linguaggio C, che implementa la ricostruzione di immagini mediche di tipo SPECT mediante pixel naturali; scegliendo le routine apposite, è possibile tenere o meno conto dell’effetto di attenuazione.