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2019
Journal article
Open Access
Inexact Arnoldi residual estimates and decay properties for functions of non-Hermitian matrices
Pozza S., Simoncini V.
This paper derives a priori residual-type bounds for the Arnoldi approximation of a matrix function together with a strategy for setting the iteration accuracies in the inexact Arnoldi approximation of matrix functions. Such results are based on the decay behavior of the entries of functions of banded matrices. Specifically, a priori decay bounds for the entries of functions of banded non-Hermitian matrices will be exploited, using Faber polynomial approximation. Numerical experiments illustrate the quality of the results.Source: BIT (Nord. Tidskr. Inf-Behandl.) 59 (2019): 969–986. doi:10.1007/s10543-019-00763-6
DOI: 10.1007/s10543-019-00763-6
DOI: 10.48550/arxiv.1605.01595
Metrics:
Pozza S., Simoncini V.
This paper derives a priori residual-type bounds for the Arnoldi approximation of a matrix function together with a strategy for setting the iteration accuracies in the inexact Arnoldi approximation of matrix functions. Such results are based on the decay behavior of the entries of functions of banded matrices. Specifically, a priori decay bounds for the entries of functions of banded non-Hermitian matrices will be exploited, using Faber polynomial approximation. Numerical experiments illustrate the quality of the results.Source: BIT (Nord. Tidskr. Inf-Behandl.) 59 (2019): 969–986. doi:10.1007/s10543-019-00763-6
DOI: 10.1007/s10543-019-00763-6
DOI: 10.48550/arxiv.1605.01595
Metrics:
See at:
arXiv.org e-Print Archive 
| BIT Numerical Mathematics | Archivio istituzionale della ricerca - Alma Mater Studiorum Università di Bologna | ISTI Repository | BIT Numerical Mathematics 
| doi.org | link.springer.com | CNR ExploRA
2018
Journal article
Open Access
The lanczos algorithm and complex gauss quadrature
Pozza S., Pranic M. S., Strakos Z.
Gauss quadrature can be naturally generalized in order to approximate quasi-definite linear functionals, where the interconnections with (formal) orthogonal polynomials, (complex) Jacobi matrices, and the Lanczos algorithm are analogous to those in the positive definite case. In this survey we review these relationships with giving references to the literature that presents them in several related contexts. In particular, the existence of the n-weight (complex) Gauss quadrature corresponds to successfully performing the first n steps of the Lanczos algorithm for generating biorthogonal bases of the two associated Krylov subspaces. The Jordan decomposition of the (complex) Jacobi matrix can be explicitly expressed in terms of the Gauss quadrature nodes and weights and the associated orthogonal polynomials. Since the output of the Lanczos algorithm can be made real whenever the input is real, the value of the Gauss quadrature is a real number whenever all relevant moments of the quasi-definite linear functional are real.Source: Electronic transactions on numerical analysis 50 (2018): 1–19. doi:10.1553/etna_vol50s1
DOI: 10.1553/etna_vol50s1
Metrics:
Pozza S., Pranic M. S., Strakos Z.
Gauss quadrature can be naturally generalized in order to approximate quasi-definite linear functionals, where the interconnections with (formal) orthogonal polynomials, (complex) Jacobi matrices, and the Lanczos algorithm are analogous to those in the positive definite case. In this survey we review these relationships with giving references to the literature that presents them in several related contexts. In particular, the existence of the n-weight (complex) Gauss quadrature corresponds to successfully performing the first n steps of the Lanczos algorithm for generating biorthogonal bases of the two associated Krylov subspaces. The Jordan decomposition of the (complex) Jacobi matrix can be explicitly expressed in terms of the Gauss quadrature nodes and weights and the associated orthogonal polynomials. Since the output of the Lanczos algorithm can be made real whenever the input is real, the value of the Gauss quadrature is a real number whenever all relevant moments of the quasi-definite linear functional are real.Source: Electronic transactions on numerical analysis 50 (2018): 1–19. doi:10.1553/etna_vol50s1
DOI: 10.1553/etna_vol50s1
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Electronic Transactions on Numerical Analysis | Electronic Transactions on Numerical Analysis | etna.math.kent.edu | ISTI Repository | CNR ExploRA
2017
Report
Open Access
Kernel PCA for novelty detection
Pozza S.
Novelty detection indexes are used in order to identify anomaly in the observation of a phenomenon. We describe the basic idea of kernel principal component analysis, a method which enlightens the existence of a novelty in a measured value comparing it with the one predicted by a model calibrated on training data. Differently from linear PCA, kernel PCA projects the data into an infinite-dimensional space in which novelty detection has usually a better performance.Source: ISTI Technical reports, 2017
Pozza S.
Novelty detection indexes are used in order to identify anomaly in the observation of a phenomenon. We describe the basic idea of kernel principal component analysis, a method which enlightens the existence of a novelty in a measured value comparing it with the one predicted by a model calibrated on training data. Differently from linear PCA, kernel PCA projects the data into an infinite-dimensional space in which novelty detection has usually a better performance.Source: ISTI Technical reports, 2017
See at:
ISTI Repository | CNR ExploRA
2017
Contribution to conference
Open Access
Stability of network indexes defined through matrix functions
Pozza S., Tudisco F.
Stability of network indexes defined trough matrix functions.Source: Due giorni di "Algebra lineare numerica", Como, Italy, 16-17 February 2017
Pozza S., Tudisco F.
Stability of network indexes defined trough matrix functions.Source: Due giorni di "Algebra lineare numerica", Como, Italy, 16-17 February 2017
See at:
ISTI Repository | CNR ExploRA
2017
Report
Unknown
MOSCARDO - Tecnologie ICT per il MOnitoraggio Strutturale di Costruzioni Antiche basato su Reti di sensori wireless e DrOni [MMS Lab, Rapporto tecnico n.1]
Girardi M., Padovani C., Pellegrini D., Pozza S.
MOSCARDO - ICT technologies for structural monitoring of age-old constructions based on wireless sensor networks and drones. Description of the activities conducted by the Mechanics of Materials and Structures Laboratory of ISTI-CNR. Project Report n. 1Source: Project report, MOSCARDO, 2017
Girardi M., Padovani C., Pellegrini D., Pozza S.
MOSCARDO - ICT technologies for structural monitoring of age-old constructions based on wireless sensor networks and drones. Description of the activities conducted by the Mechanics of Materials and Structures Laboratory of ISTI-CNR. Project Report n. 1Source: Project report, MOSCARDO, 2017
See at: CNR ExploRA