Journal publications

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• N. Guglielmi, R. Guerrieri, G. Baccarani: Highly-Constrained Neural Networks for Industrial Quality Control , IEEE Transactions on Neural Networks, 7, no. 1, pp. 206--213, 1996.
• N. Guglielmi: Inexact Newton methods for the steady-state analysis of nonlinear circuits , Mathematical Models and Methods in Applied Sciences, 6, no. 1, pp. 43--57, 1996.
• A. Montanari, N. Guglielmi: Gli indici di proiezione nella projection pursuit , Statistica, LVI, no. 1, pp. 63--86, 1996.
• N. Guglielmi: On the asymptotic stability properties of Runge-Kutta methods for delay differential equations , Numerische Mathematik, 77, no. 4, pp. 467--485, 1997.
• A. Bellen, N. Guglielmi and L. Torelli: Asymptotic stability properties of Θ-methods for the pantograph equation , Applied Numerical Mathematics, 24, no. 2--3, pp. 279--293, 1997.
• N. Guglielmi: Delay dependent stability regions of Θ-methods for delay differential equations , IMA Journal of Numerical Analysis, 18, pp. 399--418, 1998.
• A. Bellen, N. Guglielmi and M. Zennaro: On the contractivity and asymptotic stability of systems of delay differential equations of neutral type , BIT, 39, pp. 1--24, 1999.
• A. Bellen, N. Guglielmi and A. Ruehli: Methods for linear systems of circuit delay differential equations of neutral type , IEEE Transactions on Circuits and Systems-I: Fundamental theory and applications, 46, no. 1, pp. 212--216, 1999.
• N. Guglielmi and E. Hairer: Order stars and stability for delay differential equations , Numerische Mathematik, 83, no. 3, pp. 371--383, 1999.
• N. Guglielmi: An analytic proof of numerical stability of Gaussian collocation for delay differential equations , Boll. UMI Sez. B., 1-B, pp.95--116, 2000.
• N. Guglielmi and E. Hairer: Geometric proofs of numerical stability for delay equations , IMA Journal of Numerical Analysis, 21, no. 1, pp. 439--450, 2001.
• N. Guglielmi and M. Zennaro: On the zero-stability of variable stepsize multistep methods: the spectral radius approach , Numerische Mathematik, 88, no. 3, pp. 445--458, 2001.
• N. Guglielmi: On the qualitative behaviour of numerical methods for delay differential equations of neutral type. A case study: Θ-methods , Recent Trends in Numerical Analysis, edited by L. Brugnano and D. Trigiante.
• N. Guglielmi and M. Zennaro: On the asymptotic properties of a family of matrices , Linear Algebra and its Applications, 322, no. 1--3, pp. 169--192, 2001.
• A. Bellen, N. Guglielmi and M. Zennaro: Numerical stability of nonlinear delay differential equations of neutral type , Journal of Computational and Applied Mathematics, 125, no. 1--2, pp. 251--263, 2001.
• N. Guglielmi and E. Hairer: Implementing Radau IIA methods for stiff delay differential equations , Computing, 67, no. 1, pp. 1--12, 2001.
• N. Guglielmi: Asymptotic stability barriers for natural Runge--Kutta processes for delay equations , SIAM Journal on Numerical Analysis, 39, no. 3, pp. 763--783, 2002.
• N. Guglielmi and M. Zennaro, On the limit products of a family of matrices , Linear Algebra and its Applications, 362, pp. 11--27, 2003.
• N. Guglielmi and M. Zennaro: Stability of one-leg Θ-methods for the variable coefficient pantograph equation , IMA Journal on Numerical Analysis, 23, pp 421--438, 2003.
• N. Guglielmi: Open issues in devising software for the numerical solution of implicit delay differential equations , Journal of Computational and Applied Mathematics, 185, pp. 261-277, 2006.
• N. Guglielmi: On the Newton iteration in the application of collocation methods to implicit delay equations , Applied Numerical Mathematics, 53, pp. 281--297, 2005.
• N. Guglielmi and C. Lubich: Numerical periodic orbits of neutral delay differential equations , Discrete and Continuous Dynamical Systems - Series A (DCDS-A), 13, pp. 1057--1067, 2005.
• N. Guglielmi: Short proofs and a counterexample for analytical and numerical stability of delay equations with infinite memory , IMA Journal on Numerical Analysis, 26, pp. 60--77, 2006.
• N. Guglielmi, F. Wirth and M. Zennaro: Complex polytope extremality results for families of matrices , SIAM Journal on Matrix Analysis and Applications, 27, pp 721--743, 2005.
• G. Bellettini, G. Fusco and N. Guglielmi: A concept of solution and numerical experiments for forward-backward diffusion equations , Discrete and Continuous Dynamical Systems - Series A (DCDS-A), 16, pp. 783--842, 2006.
• A. Bellen, N. Guglielmi and S. Maset: Numerical methods for delay models in biomathematics , in Integration of Complex Systems in Biomedicine, A. Quarteroni (editor), Springer Verlag {pp 148--185, 2006.
• N. Guglielmi e M. Zennaro: Balanced complex polytopes and related vector and matrix norms , Journal of Convex Analysis, 14, pp. 729--766, 2007.
• Y. Muroya, E. Ishiwata and N. Guglielmi: Global stability for nonlinear difference equations with variable coefficients , Journal of Mathematical Analysis and its Applications, 334, pp. 232--247, 2007.
• N. Guglielmi and E. Hairer: Computing breaking points in implicit delay differential equations , Advances in Computational Mathematics, 29, pp. 229--247, 2008.
• N. Guglielmi and M. Zennaro: An algorithm for finding extremal polytope norms of matrix families , Linear Algebra and its Applications, 428, pp. 2265--2282, 2008.
• N. Guglielmi and L. Hatvani: On small oscillations of dynamical systems with time-dependent kinetic and potential energy , Discrete and Continuous Dynamical Systems - Series A (DCDS-A), 20, pp. 911--926 , 2008.
• A. Bellen and N. Guglielmi: Solving neutral delay differential equations with state-dependent delays , Journal of Computational and Applied Mathematics, 229, pp. 350--362 , 2009.
• A. Bellen, N. Guglielmi, S. Maset and M. Zennaro: Recent trends in the numerical solution of retarded functional differential equations , Acta Numerica 2009, pp 1--110, 2009.
• N. Guglielmi and M. Zennaro: Finding extremal complex polytope norms for families of real matrices , SIAM Journal on Matrix Analysis and Applications, 31, pp. 602--620, 2009.
• A. Cicone, N. Guglielmi, S. Serra and M. Zennaro: Finiteness properties of 2-by-2 sign-matrices via real polytope extremal norms , Linear Algebra and its Applications, 432, pp. 796--816, 2010.
• J. De Luca, N. Guglielmi, T. Humphries and A. Politi: Electromagnetic two-body problem: recurrent dynamics in the presence of state-dependent delay , Journal of Physics A: Mathematical and Theoretical, 43, 2010.
• N. Guglielmi, C. Manni and D. Vitale: Convergence analysis of C² Hermite interpolatory subdivision schemes by explicit joint spectral radius formulas , Linear Algebra and its Applications, 434, pp. 884--902, 2011.
• G. Fusco and N. Guglielmi: A regularization for discontinuous differential equations with application to state-dependent delay differential equations , Journal of Differential Equations, 250, pp. 3230--3279, 2011.
• N. Guglielmi and C. Lubich: Differential equations for roaming pseudospectra: paths to extremal points and boundary tracking , SIAM Journal on Numerical Analysis, 49, pp. 1194--1209, 2011.
• N. Guglielmi and M. Overton: Fast algorithms for the approximation of the pseudospectral abscissa and pseudospectral radius of a matrix , SIAM Journal on Matrix Analysis and Applications, 32, pp. 1166--1192, 2011.
• N. Guglielmi and M. Zennaro: On the asymptotic regularity of a family of matrices , Linear Algebra and its Applications, 436, pp. 2093--2104, 2012.
• N. Guglielmi and C. Lubich: Erratum/Addendum: Differential Equations for Roaming Pseudospectra: Paths to Extremal Points and Boundary Tracking , SIAM Journal on Numerical Analysis, 50, pp. 977--981, 2012.
• N. Guglielmi and E. Hairer: Numerical approaches for state-dependent neutral delay equations with discontinuities , Mathematics and Computers in Simulation, {(published online, 9 December 2011, available at address http://www.sciencedirect.com/science/article/pii/S0378475411002667).
• N. Guglielmi and E. Hairer: Asymptotic expansions for regularized state-dependent neutral delay equations , SIAM Journal on Mathematical Analysis, 44, pp. 2428--2458, 2012.
• N. Guglielmi and V.Yu. Protasov, Exact computation of joint spectral characteristics of linear operators , Foundations of Computational Mathematics'', 13(1)2013, p.37--97, 2013.
• W. Michiels and N. Guglielmi: An iterative method for computing the pseudospectral abscissa for a class of nonlinear eigenvalue problems , SIAM Journal on Scientific Computing, 34, pp. 2366--2393, 2012.
• P. Buttà, N. Guglielmi, S. Noschese: Computing the structured pseudospectrum of a Toeplitz matrix and its extremal points , SIAM Journal on Matrix Analysis and Applications, 33, pp. 1300--1319, 2012.
• N. Guglielmi and C. Lubich: Low-rank dynamics for computing extremal points of real pseudospectra , SIAM Journal on Matrix Analysis and Applications, 34(1), pp. 40--66, 2013.
• N. Guglielmi: Delay differential equations , Encyclopedia of Applied and Computational Mathematics, delivered January 2012.
• L. Dieci and N. Guglielmi: Regularizing piecewise smooth differential systems: co-dimension 2 discontinuity surface , Journal of Dynamics and Differential Equations, 25(1), pp. 71--94, 2013.
• N. Guglielmi and E. Hairer: Regularization of neutral delay differential equations with several delays , Journal of Dynamics and Differential Equations, 25(1), pp. 173--192, 2013.
• N. Guglielmi, M. Gurbuzbalaban and M.L. Overtoon: Fast Approximation of the H-infinity norm via optimization over spectral value sets , SIAM Journal on Matrix Analysis and Applications, 34, pp. 709--737, 2013.
• R. Jungers, A. Cicone and N. Guglielmi: Lifted polytope methods for computing the joint spectral radius , SIAM Journal on Matrix Analysis and Applications, 35, pp. 391--410, 2014.
• D. Verhees, R. Van Beeumen, K. Meerbergen, N. Guglielmi and W. Michiels Fast algorithms for computing the distance to instability of nonlinear eigenvalue problems, with application to time-delay systems , International Journal of Dynamics and Control, in press, 2014.
• N. Guglielmi, D. Kressner and C. Lubich: Computing extremal points of symplectic pseudospectra and solving symplectic matrix nearness problems , SIAM Journal on Matrix Analysis and Applications, 35(4), pp. 1407--1428, 2014.
• N. Guglielmi, D. Kressner and C. Lubich: Low-rank differential equations for Hamiltonian matrix nearness problems , Numerische Mathematik, 129(2), pp. 279--319, 2015.
• P. Buttà, N. Guglielmi, M. Manetta, S. Noschese: Differential equations for real-structured (and unstructured) defectivity measures , SIAM Journal on Matrix Analysis and Applications, 36(2), pp. 523--548, 2015.
• N. Guglielmi and M. Zennaro, Canonical construction of Barabanov polytope norms and antinorms for sets of matrices , SIAM Journal on Matrix Analysis and Applications, 36(2), pp. 634--655, 2015.
• N. Guglielmi and M. Manetta: Approximating real stability radii , IMA Journal of Numerical Analysis, 35, pp. 1402--1425, 2015.
• N. Guglielmi, M. Overton, G.W. Stewart: An efficient algorithm for computing the Generalized Null Space Decomposition , SIAM Journal on Matrix Analysis and Applications, 36(1), pp. 38--54, 2015.
• N. Guglielmi, L. Laglia and V.Yu. Protasov, Polytope Lyapunov functions for stable and for stabilizable LSS , Foundations of Computational Mathematics, in press, 2015.
• N. Guglielmi and E. Hairer: Path regularization of linear neutral delay differential equations with several delays , Journal of Computational and Applied Mathematics, in press, 2015.
• N. Guglielmi and E. Hairer: Classification of hidden dynamics in discontinuous dynamical systems , SIAM Journal on Applied Dynamical Systems, in press, 2015.
• N. Guglielmi and M. Manetta: An iterative method for computing robustness of polynomial stability , Journal of Computational and Applied Mathematics, in press, 2015
• N. Guglielmi and V.Yu. Protasov, Invariant polytopes of sets of matrices with application to regularity of wavelets and subdivisions , SIAM Journal on Matrix Analysis and Applications, in press, 2015.

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Preprints

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• N. Guglielmi: On the method by Rostami for computing the real stability radius of large and sparse matrices , submitted, 2015
• C. Conti, M. Charina, N. Guglielmi and V.Yu. Protasov: Regularity of non-stationary multivariate subdivision , submitted, 2015