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.
- hubauth: Computation of the hub/authority centrality of the nodes of a network.
- lbdtik: Tikhonov regularization by Lanczos bidiagonalization.
- orthomoms: a Matlab toolbox for the computation of the orthogonal moments of an image.
- pqser: a Matlab package for spectral seriation.
- sgcen: Computation of the subgraph centrality of the nodes of an undirected network.
- smt: Structured matrices toolbox.
- toms729gw: Fast solver for Toeplitz linear systems.
- tpls: Fast least squares solver for Toeplitz linear systems.

**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.

*arXiv:1803.00638 [math.NA]*, 2018.

- 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, 2018.

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