Index:

- blgaussexp: Computation of the subgraph centrality of the nodes of a directed network
- corner.m: Find the corner of a discrete L-curve
- cosereg: Regularization by the Comparison of Solutions Estimator (COSE) method
- drsolve: Solver for linear systems with displacement structure
- ErresTools: Choosing a regularization parameter by error estimation
- FDEMtools: A MATLAB package for EMI data inversion
- hubauth: Computation of the hub/authority centrality of the nodes of a network
- lbdtik: Tikhonov regularization by Lanczos bidiagonalization
- mngn: Minimal norm solution of a nonlinear least squares problem
- orthomoms: A Matlab toolbox for the computation of the orthogonal moments of an image
- pqser: A Matlab package for spectral seriation
- rbc: Recursive computation of the broadcast centrality
- sgcen: Computation of the subgraph centrality of the nodes of an undirected network
- smt: Structured matrices toolbox
- specbip: A spectral method for bipartizing a network and detecting a large anti-community
- toms729gw: Fast solver for Toeplitz linear systems
- tpls: Fast least squares solver for Toeplitz linear systems

**rbc**-
**Recursive computation of the broadcast centrality.**The software is described in the paper

Authors: M. Al Mugahwi, O. De La Cruz Cabrera, C. Fenu, L. Reichel, and G. Rodriguez.

- M. Al Mugahwi, O. De La Cruz Cabrera, C. Fenu, L. Reichel, and G.
Rodriguez.

Block matrix models for dynamic networks.

Appl. Math. Comput., to appear, 2021.

- M. Al Mugahwi, O. De La Cruz Cabrera, C. Fenu, L. Reichel, and G.
Rodriguez.
**mngn**-
**mngn: minimal norm solution of a nonlinear least squares problem.**This Matlab package implements the algorithms described in the paper

Authors: F. Pes and G. Rodriguez.

- F. Pes and G. Rodriguez.

The minimal norm Gauss-Newton method and some of its regularized variants.

*Electron. Trans. Numer. Anal.*, 53:459-480, 2020.

DOI: 10.1553/etna_vol53s459

Last updated: February 19, 2021. - F. Pes and G. Rodriguez.
**specbip**-
**specbip: a spectral method for bipartizing a network and detecting a large anti-community.**This function approximates a given network by a bipartite one. The algorithm produces a node permutation which makes the possible bipartite nature of the initial adjacency matrix evident, and identifies the two sets of nodes. The same procedure can be used to detect the presence of a large anti-community in a network and to identify it. The toolbox is described in the paper

Authors: A. Concas, S. Noschese, L. Reichel, and G. Rodriguez.

- A. Concas, S. Noschese, L. Reichel, and G. Rodriguez.

A spectral method for bipartizing a network and detecting a large anti-community.

*J. Comput. and Appl. Math.*, 2020.

DOI: 10.1016/j.cam.2019.06.022

- A. Concas, S. Noschese, L. Reichel, and G. Rodriguez.
**FDEMtools**-
**FDEMtools: a MATLAB package for FDEM data inversion.**This package provides a set of Matlab functions to solve a non-linear electromagnetic data inversion problem. Starting from electromagnetic data collected by a ground conductivity meter, we reconstruct either the electrical conductivity or the magnetic permeability of the soil with respect to depth by a regularized Gauss-Newton method. The inversion algorithm is based on the low-rank approximation of the Jacobian of the nonlinear model, which depends both on a relaxation parameter and a regularization parameter, chosen by automatic procedures.

Authors: G. P. Deidda, P. Díaz De Alba, C. Fenu, G. Lovicu, and G. Rodriguez

The package is described in the paper:- G. P. Deidda, P. Díaz De Alba, C. Fenu, G. Lovicu, and G. Rodriguez

FDEMtools: a MATLAB package for FDEM data inversion.

*Numer. Algorithms*, 2020.

DOI: 10.1007/s11075-019-00843-2

- G. P. Deidda, C. Fenu, and G. Rodriguez.

Regularized solution of a nonlinear problem in electromagnetic sounding.

*Inverse Problems*, 30:125014 (27 pages), 2014.

DOI: 10.1088/0266-5611/30/12/125014 - P. Díaz De Alba and G. Rodriguez.

Regularized inversion of multi-frequency EM data in geophysical applications.

In F. Ortegón Gallego, M.V. Redondo Neble, and J.R. Rodríguez Galván, editors, Trends in Differential Equations and Applications, volume 8 of SEMA SIMAI Springer Series, pages 357-369. Springer, Switzerland, 2016.

- G.P. Deidda, P. Díaz De Alba, and G. Rodriguez.

Identifying the magnetic permeability in multi-frequency EM data inversion.

*Electron. Trans. Numer. Anal.*, 47:1-17, 2017.

Last updated: August 15, 2018. - G. P. Deidda, P. Díaz De Alba, C. Fenu, G. Lovicu, and G. Rodriguez
**cosereg**-
**cosereg: regularization by the Comparison of Solutions Estimator (COSE) method.**The Comparison of Solution Estimator (COSE) is a strategy for choosing the regularization parameter by comparing the results of different methods. One of the functions in the toolbox is intended for small scale problems, the others are for large scale problems. Both standard and general form can be treated.

Authors: M. E. Hochstenbach, Y. Park, L. Reichel, G. Rodriguez, and X. Yu.

The algorithms are described in the papers:- M. E. Hochstenbach, L. Reichel, and G. Rodriguez.

Regularization parameter determination for discrete ill-posed problems.

*J. Comput. and Appl. Math.*, 273:132-149, 2015.

DOI: 10.1016/j.cam.2014.06.004 - Y. Park, L. Reichel, G. Rodriguez, and X. Yu.

Parameter determination for Tikhonov regularization problems in general form.

*J. Comput. and Appl. Math.*, 343:12-25, 2018.

DOI: 10.1016/j.cam.2018.04.049

Last updated: May 6, 2018. - M. E. Hochstenbach, L. Reichel, and G. Rodriguez.
**orthomoms**-
**orthomoms: a Matlab toolbox for the computation of the orthogonal moments of an image.**The functions in this package allow the computation of the moments of an image with respect to Legendre, discrete Chebyshev, and second kind Chebyshev orthogonal polynomials. The orthogonal moments are intended to be used as descriptors for image classification. The toolbox is described in the paper

Authors: C. Di Ruberto, L. Putzu, and G. Rodriguez.

- C. Di Ruberto, L. Putzu, and G. Rodriguez.

Fast and accurate computation of orthogonal moments for texture analysis.

*Pattern Recongnit.*, 83:498-510, 2018.

DOI: 10.1016/j.patcog.2018.06.012

- C. Di Ruberto, L. Putzu, and G. Rodriguez.
**pqser**-
**pqser: a Matlab package for spectral seriation.**This toolbox contains an implementation of an algorithm to solve the seriation problem. It also implements a data structure for PQ trees. The toolbox is described in the paper

Authors: A. Concas, C. Fenu, and G. Rodriguez.

- A. Concas, C. Fenu, and G. Rodriguez.

pqser: a Matlab package for spectral seriation

*Numer. Algorithms*, 80(3):879-902, 2019.

DOI: 10.1007/s11075-018-0510-6

- J. E. Atkins, E. G. Boman, and B. Hendrickson.

A spectral algorithm for seriation and the consecutive ones problem.

*SIAM J. Comput.*, 28(1):297-310, 1998.

- A. Concas, C. Fenu, and G. Rodriguez.
**blgaussexp**-
**Computation of the subgraph centrality of the nodes of a directed network.**This set of functions allows the computation of the subgraph communicabilities between the nodes of a network, either undirected or directed, as well as the starting/ending convenience. The computation of is performed by block Gauss/Anti-Gauss quadrature. The functions were developed for Matlab, but they are compatible with Octave. They are described in the paper

Authors: C. Fenu, D. Martin, L. Reichel, and G. Rodriguez.

- C. Fenu, D. Martin, L. Reichel, and G. Rodriguez.

Block Gauss and anti-Gauss quadrature with application to networks.

*SIAM J. Matrix Anal. Appl.,*, 34(4):1655-1684, 2013.

DOI: 10.1137/120886261

- C. Fenu, D. Martin, L. Reichel, and G. Rodriguez.
**hubauth**-
**Computation of the hub/authority centrality of the nodes of a network.**This set of functions allows the computation of the hub/authority centrality of the nodes of a network by three different algorithms: Gauss quadrature, low-rank approximation, and a hybrid method. The functions were developed for Matlab, but they are compatible with Octave. They are described in the paper

Authors: J. Baglama, C. Fenu, L. Reichel, and G. Rodriguez.

- J. Baglama, C. Fenu, L. Reichel, and G. Rodriguez.

Analysis of directed networks via partial singular value decomposition and Gauss quadrature.

*Linear Algebra Appl.*, 456:93-121, 2014.

DOI: 10.1016/j.laa.2014.05.018

`irlba`described in the paper- J. Baglama and L. Reichel.

Augmented implicitly restarted Lanczos bidiagonalization methods.

*SIAM J. Sci. Comput.*, 27:19-42, 2005.

`irblsvds_leja`, from- J. Baglama and L. Reichel.

An implicitly restarted block Lanczos bidiagonalization method using Leja shifts.

*BIT*, 53:285-310, 2013.

Last updated: July 4, 2014. - J. Baglama, C. Fenu, L. Reichel, and G. Rodriguez.
**sgcen**-
**Computation of the subgraph centrality of the nodes of an undirected network.**This set of functions allows the computation of the subgraph centrality of the nodes of a network. The functions were developed for Matlab, but they are compatible with Octave. They are described in the paper

Authors: C. Fenu, D. Martin, L. Reichel, and G. Rodriguez.

- C. Fenu, D. Martin, L. Reichel, and G. Rodriguez.

Network analysis via partial spectral factorization and Gauss quadrature.

*SIAM J. Sci. Comput.*, 35(4):A2046-A2068, 2013.

DOI: 10.1137/130911123

`irbleigs`from- J. Baglama, D. Calvetti, and L. Reichel.

Algorithm 827: irbleigs: A MATLAB program for computing a few eigenpairs of a large sparse Hermitian matrix.

*ACM Trans. Math. Software*, 29:337-348, 2012.

- C. Fenu, D. Martin, L. Reichel, and G. Rodriguez.
**smt**-
**Structured matrices toolbox.**smt is a Matlab toolbox for structured matrix computation.

Authors: M. Redivo-Zaglia and G. Rodriguez.

For documentation, see- M. Redivo-Zaglia and G. Rodriguez.

`smt`: a Matlab structured matrices toolbox.

*Numer. Algorithms*, 59(4):639-659, 2012.

DOI: 10.1007/s11075-011-9527-9

- M. Redivo-Zaglia and G. Rodriguez.
**drsolve**-
**Solver for linear systems with displacement structure.**This package provides a set of Matlab functions to solve linear systems whose matrix belongs to the following classes: Cauchy-like, Toeplitz-like, Toeplitz+Hankel-like and Vandermonde-like. The solvers have a computational cost

Authors: A. Aricò and G. Rodriguez.

*O(rn*, and use^{2})*O(rn)*memory locations, where*n*is the size and*r*is the displacement rank of the matrix.

See- A. Aricò and G. Rodriguez.

A fast solver for linear systems with displacement structure.

*Numer. Algorithms*, 55(4):529-556, 2010.

DOI: 10.1007/s11075-010-9421-x

- A. Aricò and G. Rodriguez.
**ErresTools**-
**Choosing a regularization parameter by error estimation.**This small Matlab toolbox contains some functions for determining a suitable value of the regularization parameter in TSVD and Tikhonov regularization by employing the error estimates described in the papers

Authors: G. Rodriguez.

- C. Brezinski, G. Rodriguez, and S. Seatzu.

Error estimates for linear systems with applications to regularization.

*Numer. Algorithms*, 49(1-4):85-104, 2008.

DOI: 10.1007/s11075-008-9163-1 - C. Brezinski, G. Rodriguez, and S. Seatzu.

Error estimates for the regularization of least squares problems.

*Numer. Algorithms*, 51(1):61-76, 2009.

DOI: 10.1007/s11075-008-9243-2

Last updated: March 10, 2010. - C. Brezinski, G. Rodriguez, and S. Seatzu.
**toms729gw**-
**Fast solver for Toeplitz linear systems.**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

Authors: A. Aricò and G. Rodriguez (for the Matlab MEX gateway).

Authors: P.C. Hansen and T. Chan (for the computational routines).

- P.C. Hansen and T. Chan.

FORTRAN subroutines for general Toeplitz systems

*ACM Trans. Math. Software*, 18(3):256-273, 1992.

- P.C. Hansen and T. Chan.
**lbdtik**-
**Tikhonov regularization by Lanczos bidiagonalization.**This Matlab function computes the Tikhonov regularized solution a linear system, choosing the regularization parameter by minimizing an estimate of the error. A test driver, (which requires the Regularization Tools) is included. The algorithm is described in the paper

Authors: L. Reichel and G. Rodriguez.

- L. Reichel, G. Rodriguez, and S. Seatzu.

Error estimates for large-scale ill-posed problems.

*Numer. Algorithms*, 51(3):341-361, 2009.

DOI: 10.1007/s11075-008-9244-1

- L. Reichel, G. Rodriguez, and S. Seatzu.
**tpls**-
**Fast least squares solver for Toeplitz linear systems.**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

Author: G. Rodriguez.

- G. Rodriguez.

Fast solution of Toeplitz- and Cauchy-like least squares problems.

*SIAM J. Matrix Anal. Appl.,*, 28(3):724-748, 2006.

DOI: 10.1137/050629148

- G. Rodriguez.
**corner.m**-
**Find the corner of a discrete L-curve.**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

Authors: P.C. Hansen, T.K. Jensen, and G. Rodriguez.

- P.C. Hansen, T.K. Jensen, and G. Rodriguez.

An adaptive pruning algorithm for the discrete L-curve criterion.

*J. Comput. and Appl. Math.*, 198(2):483-492, 2007.

DOI: 10.1016/j.cam.2005.09.026

Last updated: January 11, 2007. - P.C. Hansen, T.K. Jensen, and G. Rodriguez.

Giuseppe Rodriguez

rodriguez@unica.it