Index:

- blgaussexp: Computation of the subgraph centrality of the nodes of a directed network.
- corner.m Find the corner of a discrete L-curve.
- 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.
- 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.

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

Error estimates for the regularization of least squares problems.

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

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 Transactions on Mathematical Software (TOMS)*, 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.

- 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. Matr. Anal. Appl.*, 28(3):724-748, 2006..

- 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.

*Journal of Computational and Applied Mathematics*, 198(2):483-492, 2007.

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

Giuseppe Rodriguez

rodriguez@unica.it