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Nicola Guglielmi
Nicola Guglielmi
Full Professor
Mathematics and Applications
MAT/08 - Analisi numerica
Numerical and Computational Methods
Coppito 1, Room
guglielm@univaq.it
Download curriculum vitae
Research
Teaching
Publications
Work areas
Numerical methods for retarded differential equations.
Computation of the joint spectral radius of a family of matrices.
Pseudospectral computation and related stability measures.
Stability of numerical methods for differential equations.
Switched systems.
Numerical methods for discontinuous differential equations and regularizations.
Regularization of forward backward parabolic partial differential equations.
Stiff delay equations
Scholarpedia introduction
.
Teaching web pages:
http://univaq.it/~guglielm/
Office hours:
Wednesday 15:00 - 17:00
Click here to read the curriculum vitae of Nicola Guglielmi
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 C
2
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, in press, 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, in press, 2013.
N. Guglielmi and E. Hairer:
Regularization of neutral delay differential equations with several delays
, Journal of Dynamics and Differential Equations, in press, 2013.
Preprints
Fast Approximation of the H-infinity norm via optimization over spectral value sets
, SIAM Journal on Matrix Analysis and Applications, accepted for publication, 2013.
N. Guglielmi, D. Kressner and C. Lubich:
Low-rank differential equations for Hamiltonian matrix nearness problems
, submitted, Numerische Mathematik.