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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

**See at: **
BIT Numerical Mathematics | ISTI Repository | BIT Numerical Mathematics | BIT Numerical Mathematics | BIT Numerical Mathematics | BIT Numerical Mathematics | BIT Numerical Mathematics | 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

**See at: **
ETNA - Electronic Transactions on Numerical Analysis | etna.math.kent.edu | ISTI Repository | CNR ExploRA | ETNA - Electronic Transactions on Numerical Analysis | ETNA - Electronic Transactions on Numerical Analysis

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

**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

**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. 1**Source: **Project report, MOSCARDO, 2017

**See at: **
CNR ExploRA