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2017
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Open Access
NOSA-ITACA documentation. Version 1.1
Binante V., Girardi M., Padovani C., Pasquinelli G., Pellegrini D., Porcelli M., Robol L.
NOSA-ITACA is a code for the nonlinear structural analysis of historical masonry constructions. It the result of the integration of the finite element code NOSA into the open-source SALOME platform.DOI: 10.32079/isti-tr-2017/001
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Binante V., Girardi M., Padovani C., Pasquinelli G., Pellegrini D., Porcelli M., Robol L.
NOSA-ITACA is a code for the nonlinear structural analysis of historical masonry constructions. It the result of the integration of the finite element code NOSA into the open-source SALOME platform.DOI: 10.32079/isti-tr-2017/001
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CNR IRIS 
| ISTI Repository | www.nosaitaca.it | CNR IRIS 
2017
Conference article
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NOSA-ITACA: a free FE program for historic masonry buildings
Girardi M, Padovani C, Pellegrini D, Robol L
This paper describes the main features of NOSA-ITACA, a finite-element code for the structural analysis of masonry constructions of historical interest and reports on its application to the structural analysis of some historic buildings in Italy.
Girardi M, Padovani C, Pellegrini D, Robol L
This paper describes the main features of NOSA-ITACA, a finite-element code for the structural analysis of masonry constructions of historical interest and reports on its application to the structural analysis of some historic buildings in Italy.
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CNR IRIS | CNR IRIS | www.eccomas.org
2017
Contribution to book
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Solving large scale quasiseparable Lyapunov equations
Massei S, Palitta D, Robol L
We consider the problem of efficiently solving Lyapunov and Sylvester equations of medium and large scale, in the case where all the coefficients are quasiseparable, i.e., they have off-diagonal blocks of low-rank. This comprises the case with banded coefficients and right-hand side, recently studied in [6, 9]. We show that, under suitable assumptions, this structure is guaranteed to be numer- ically present in the solution, and we provide explicit estimates of the numerical rank of the off-diagonal blocks. Moreover, we describe an efficient method for approximating the solution, which relies on the technology of hierarchical matrices. A theoretical characterization of the quasiseparable structure in the solution is pre- sented, and numerically experiments confirm the applicability and efficiency of our ap- proach. We provide a MATLAB toolbox that allows easy replication of the experiments and a ready-to-use interface for our solver.
Massei S, Palitta D, Robol L
We consider the problem of efficiently solving Lyapunov and Sylvester equations of medium and large scale, in the case where all the coefficients are quasiseparable, i.e., they have off-diagonal blocks of low-rank. This comprises the case with banded coefficients and right-hand side, recently studied in [6, 9]. We show that, under suitable assumptions, this structure is guaranteed to be numer- ically present in the solution, and we provide explicit estimates of the numerical rank of the off-diagonal blocks. Moreover, we describe an efficient method for approximating the solution, which relies on the technology of hierarchical matrices. A theoretical characterization of the quasiseparable structure in the solution is pre- sented, and numerically experiments confirm the applicability and efficiency of our ap- proach. We provide a MATLAB toolbox that allows easy replication of the experiments and a ready-to-use interface for our solver.
See at:
cmmse.usal.es | CNR IRIS | CNR IRIS
2017
Journal article
Open Access
Fast Hessenberg reduction of some rank structured matrices
Gemignani L, Robol L
We develop two fast algorithms for Hessenberg reduction of a structured matrix $A = D + UV^H$, where $D$ is a real or unitary n x n diagonal matrix and $U, V in mathbb{C}^{n times k}$. The proposed algorithm for the real case exploits a two-stage approach by first reducing the matrix to a generalized Hessenberg form and then completing the reduction by annihilation of the unwanted subdiagonals. It is shown that the novel method requires O(n^2 k) arithmetic operations and is significantly faster than other reduction algorithms for rank structured matrices. The method is then extended to the unitary plus low rank case by using a block analogue of the CMV form of unitary matrices. It is shown that a block Lanczos-type procedure for the block tridiagonalization of Re(D) induces a structured reduction on A in a block staircase CMV-type shape. Then, we present a numerically stable method for performing this reduction using unitary transformations and show how to generalize the subdiagonal elimination to this shape, while still being able to provide a condensed representation for the reduced matrix. In this way the complexity still remains linear in k and, moreover, the resulting algorithm can be adapted to deal efficiently with block companion matrices.Source: SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, vol. 38 (issue 2), pp. 574-598
DOI: 10.1137/16m1107851
DOI: 10.48550/arxiv.1612.04196
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Gemignani L, Robol L
We develop two fast algorithms for Hessenberg reduction of a structured matrix $A = D + UV^H$, where $D$ is a real or unitary n x n diagonal matrix and $U, V in mathbb{C}^{n times k}$. The proposed algorithm for the real case exploits a two-stage approach by first reducing the matrix to a generalized Hessenberg form and then completing the reduction by annihilation of the unwanted subdiagonals. It is shown that the novel method requires O(n^2 k) arithmetic operations and is significantly faster than other reduction algorithms for rank structured matrices. The method is then extended to the unitary plus low rank case by using a block analogue of the CMV form of unitary matrices. It is shown that a block Lanczos-type procedure for the block tridiagonalization of Re(D) induces a structured reduction on A in a block staircase CMV-type shape. Then, we present a numerically stable method for performing this reduction using unitary transformations and show how to generalize the subdiagonal elimination to this shape, while still being able to provide a condensed representation for the reduced matrix. In this way the complexity still remains linear in k and, moreover, the resulting algorithm can be adapted to deal efficiently with block companion matrices.Source: SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, vol. 38 (issue 2), pp. 574-598
DOI: 10.1137/16m1107851
DOI: 10.48550/arxiv.1612.04196
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arXiv.org e-Print Archive | SIAM Journal on Matrix Analysis and Applications | epubs.siam.org | CNR IRIS | ISTI Repository | SIAM Journal on Matrix Analysis and Applications | doi.org | CNR IRIS | CNR IRIS