Research topics

  1. Polynomial an rational methods for the computation of Functions of Matrices

  2. Numerical methods for Fractional Differential Equations

  3. Krylov methods for the regularization of ill-conditioned linear systems

 

Pubblications and preprints

  1. P. Novati, Metodi polinomiali per l’approssimazione di funzioni di matrici, Technical Report, Department of Mathematics, University of Trieste, 410 (1997).

  2. P. Novati, A polynomial method based on truncating Faber series for the computation of the matrix exponential operator, Technical Report, Department of Mathematics, University of Trieste, 415 (1997).

  3. P. Novati, Metodi polinomiali per il calcolo di funzioni di matrici non simmetriche e di grandi dimensioni, U.M.I. Buletin, Series VIII, Vol. IV-A (2001), pp. 515-518.

  4. P.Novati, I.Moret, An interpolatory approximation of the matrix exponential based on Faber polynomials, Journal of Computational and Applied Mathematics, 131 (2001), pp. 361-380. preprint

  5. P.Novati, I.Moret, The computation of functions of matrices by truncated Faber series, Numerical Functional Analysis and Optimization, 22 (2001), pp. 697-719. preprint

  6. P.Novati, A polynomial method based on Fejer points for the computation of functions of nonsymmetric matrices, Applied Numerical Mathematics, 44 (2003), pp. 201-224. preprint

  7. P.Novati, Solving initial value problems by Faber polynomials, Numerical Linear Algebra with Applications, 10 (2003), pp. 247-270. preprint

  8. P.Novati, An explicit one-step method for stiff problems, Computing, 71 (2003), pp. 133-151. preprint

  9. P.Novati, I.Moret, RD-rational approximation of the matrix exponential operator, BIT, 44 (2004), pp. 595-615. preprint

  10. P.Novati, A low cost Arnoldi method for large linear initial value problems, International Journal of Computer Mathematics, 81 (2004), pp. 835-844. preprint

  11. P.Novati, I.Moret, Interpolating functions of matrices on zeros of quasi-kernel polynomials, Numerical Linear Algebra with Applications, 12 (2005), pp. 337-353. preprint

  12. P.Novati, A class of explicit one-step methods of order 2 for stiff problems, Journal of Numerical Mathematics, 13 (2005), pp. 219-236. preprint

  13. P.Novati, I.Moret, A Rational Krylov methods for solving time-periodic differential equations, Applied Numerical Mathematics, 58 (2008), pp. 212-222. preprint

  14. P.Novati, Some secant approximations for Rosenbrock W-methods, Applied Numerical Mathematics, 58 (2008), pp. 195-211. preprint

  15. P.Novati, On the construction of Restricted-Denominator Exponential W-methods, Journal of Computational and Applied Mathematics, 221 (2008), pp. 86-101. preprint

  16. P.Novati, Implementation of Lawson-Adams multistep methods for large stiff problems, preprint, 2009. Presented at DWCAA09, Canazei, Trento (Italy), September 4-9, 2009

  17. P.Novati, I.Moret, On the convergence of Krylov subspace methods for matrix Mittag-Leffler functions, SIAM J. Numer. Anal., 49 (2011), pp. 2144-2164. preprint

  18. P.Novati, Using the Restricted-Denominator rational Arnoldi method for exponential integrators, SIAM J. Matrix Anal. Appl., 32 (2011), pp. 1537-1558. preprint

  19. C.Brezinski, P.Novati, M.Redivo-Zaglia, A rational Arnoldi approach for ill-conditioned linear systems, Journal of Computational and Applied Mathematics, 263 (2012), pp. 2063-2077. preprint

  20. P.Novati, Efficient Computation of the Core Functions of Exponential Itegrators, AIP Conf. Proc. 1389 (2011), pp. 233-236. preprint

  21. P.Novati, Using the RD-rational Arnoldi method for exponential integrators, PAMM, 11 (2011), pp. 19-22.

  22. P.Novati, M.Redivo-Zaglia, M.R.Russo, Preconditioning linear systems via matrix function evaluation, Applied Numerical Mathematics 62 (2012), pp. 1804-1818. preprint

  23. P.Novati, M.R.Russo, Adaptive Arnoldi-Tikhonov regularization for image restoration, Numerical Algorithms 65 (2014), pp. 745-757. preprint

  24. P.Novati, M.R.Russo, A GCV based Arnoldi-Tikhonov regularization method,  BIT 54 (2014), pp. 501-521. preprint

  25. S.Gazzola, P.Novati, M.R.Russo, Embedded techniques for choosing the parameter in Tikhonov regularization, Numerical Linear Algebra with Applications 21 (2014), pp. 796-812. preprint

  26. S.Gazzola, P.Novati,  Automatic parameter setting for Arnoldi-Tikhonov methods, Journal of Computational and Applied Mathematics 256 (2014), pp 180-195. preprint

  27. S.Gazzola, P.Novati, Multiparameter Arnoldi-Tikhonov methods, Electronic Transactions on Numerical Analysis 40 (2013), pp. 452-475. preprint

  28. P.Novati, Numerical approximation to the fractional derivative operator, Numerische Mathematik 127 (2014), pp. 539-566. preprint

  29. L.Aceto, C.Magherini, P.Novati, Generalized Adams methods for Fractional Differential Equations, AIP Conf. Proc. 1479 (2012), pp. 250-253. preprint

  30. L.Aceto, C.Magherini, P.Novati, Fractional convolution quadrature based on generalized Adams methods, Calcolo 51 (2014), pp. 441-463. preprint

  31. L.Aceto, C.Magherini, P.Novati, On the construction and properties of m-step methods for FDEs, SIAM J. Sci. Comput. 37 (2015), pp. A653-A675. preprint

  32. S.Gazzola, P.Novati, M.R.Russo, On Krylov projection methods and Tikhonov regularization, Electronic Transactions on Numerical Analysis 44 (2015), pp. 83-123. preprint

  33. L.Aceto, C.Magherini, P.Novati, Short-term recursion for fractional differential equations, AIP Conf. Proc. 1648 (2015), pp. 020001-1-020001-4. doi: 10.1063/1.4912305

  34. S.Gazzola, P.Novati, On the inheritance of the discrete Picard condition, BIT 56 (2016), pp. 893–918. preprint

  35. P.Novati, Some properties of the Arnoldi based methods for linear ill-posed problems. SIAM J. Numer. Anal. 55 (2017), pp. 1437-1455. Preprint.

  36. I.G.A. Abdelsheed, P.Novati, The solution of fractional order epidemic model by implicit Adams methods, Appl. Math. Model. 43 (2017), pp. 78-84. preprint

  37. L.Aceto, P.Novati, Rational approximation to the fractional Laplacian operator in reaction-diffusion problems, SIAM J. Sci. Comput. 39 (2017), pp. A217-A228. Preprint

  38. I.Moret, P.Novati, Krylov subspace methods for functions of fractional differential operators. Submitted. Preprint

  39. P.Novati, A convergence result for some Krylov-Tikhonov methods, Submitted. Preprint

 

Research Software Freely Available

 

  1. heunsc.m - Matlab code based on the explicit two-stage Scaled-Runge-Kutta method for stiff initial value problems, 2005.

  2. roswb.m - Matlab code that implements some Rosenbrock-Wanner methods with Broyden’s updates for parabolic problems, 2008.

  3. rde43.m - Matlab code that implements two Exponential-Rosenbrock methods together with the Rational Arnoldi algorithm, 2008.