References
- M. Afanasjew, M. Eiermann, O.G. Ernst and S. Guettel, Implementation of a restarted Krylov subspace method for the evaluation of matrix functions., Linear Algebra Appl. 429 (2008), pp. 2293–2314. doi: 10.1016/j.laa.2008.06.029
- S. Bellavia, D. Bertaccini and B. Morini, Quasi matrix free preconditioners in optimization and nonlinear least-squares, in Numerical Analysis and Applied Mathematics, T. Simos, ed., Vol. 1281, Uppsala, July 2009. AIP, 2010, pp. 1036–1039.
- S. Bellavia, D. Bertaccini and B. Morini, Nonsymmetric preconditioner updates in Newton–Krylov methods for nonlinear systems, SIAM J. Sci. Comput. 33 (2011), pp. 2595–2619. doi: 10.1137/100789786
- M. Benzi, Preconditioning techniques for large linear systems: A survey, J. Comput. Phys. 182 (2002), pp. 418–477. doi: 10.1006/jcph.2002.7176
- M. Benzi, Localization in matrix computations: Theory and applications, in Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications, Springer, 2016, pp. 211–317.
- M. Benzi and D. Bertaccini, Approximate inverse preconditioning for shifted linear systems, BIT, Numer. Math. 43 (2003), pp. 231–244. doi: 10.1023/A:1026089811044
- M. Benzi and N. Razouk, Decay bounds and O(n) algorithms for approximating functions of sparse matrices, Electron. Trans. Numer. Anal 28 (2007), pp. 16–39.
- M. Benzi and M. Tůma, Orderings for factorized sparse approximate inverse preconditioners, SIAM J. Sci. Comput. 21 (2000), pp. 1851–1868. doi: 10.1137/S1064827598339372
- L. Bergamaschi, M. Caliari and M. Vianello, Efficient approximation of the exponential operator for discrete 2D advection–diffusion problems, Numer. Linear Algebra Appl. 10 (2003), pp. 271–289. doi: 10.1002/nla.288
- D. Bertaccini, Efficient preconditioning for sequences of parametric complex symmetric linear systems, Electron. Trans. Numer. Anal 18 (2004), pp. 49–64.
- D. Bertaccini and F. Durastante, Interpolating preconditioners for the solution of sequence of linear systems, Comput. Math. Appl. 72 (2016), pp. 1118–1130. doi: 10.1016/j.camwa.2016.06.023
- D. Bertaccini and F. Durastante, Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications, Chapman & Hall/CRC Monographs and Research Notes in Mathematics, CRC Press, London and New York, 2018.
- D. Bertaccini and S. Filippone, Approximate inverse preconditioners on high performance GPU platforms, Comp. Math. Appl. 71 (2016), pp. 693–711. doi: 10.1016/j.camwa.2015.12.008
- D. Bertaccini and F. Sgallari, Updating preconditioners for nonlinear deblurring and denoising image restoration, Appl. Numer. Math. 60 (2010), pp. 994–1006. doi: 10.1016/j.apnum.2010.06.004
- C. Canuto, V. Simoncini and M. Verani, On the decay of the inverse of matrices that are sum of Kronecker products, Linear Algebra Appl. 452 (2014), pp. 21–39. doi: 10.1016/j.laa.2014.03.029
- A.J. Carpenter, A. Ruttan and R.S. Varga, Extended numerical computations on the 1/9 conjecture in rational approximation theory, in Rational Approximation and Interpolation, P.R. Graves-Morris, E.B. Saff, and R.S. Varga, eds., Lecture Notes in Mathematics Vol. 1105, Springer-Verlag, Berlin, 1984, pp. 383–411.
- W.J. Cody, G. Meinardus and R. Varga, Chebyshev rational approximations to e−x in [0,+∞) and applications to heat-conduction problems, J. Approx. Theory 2 (1969), pp. 50–65. doi: 10.1016/0021-9045(69)90030-6
- T.A. Davis and Y. Hu, The university of Florida sparse matrix collection, ACM Trans. Math. Softw. (TOMS) 38 (2011), pp. 1.
- P.J. Davis and P. Rabinowitz, Methods of Numerical Integration, Courier Corporation, Mineola, NY, 2007.
- S. Demko, W.F. Moss and P.W. Smith, Decay rates for inverses of band matrices, Math. Comput. 43 (1984), pp. 491–499. doi: 10.1090/S0025-5718-1984-0758197-9
- N.J. Ford, D.V. Savostyanov and N.L. Zamarashkin, On the decay of the elements of inverse triangular Toeplitz matrices, SIAM J. Matrix Anal. Appl. 35 (2014), pp. 1288–1302. doi: 10.1137/130931734
- R. Garrappa and M. Popolizio, On the use of matrix functions for fractional partial differential equations, Math. Comput. Simul. 81 (2011), pp. 1045–1056. doi: 10.1016/j.matcom.2010.10.009
- N. Hale, N.J. Higham and L.N. Trefethen, Computing Aαlog(A), and related matrix functions by contour integrals, SIAM J. Numer. Anal. 46 (2008), pp. 2505–2523. doi: 10.1137/070700607
- N.J. Higham, Functions of Matrices. Theory and Computation, SIAM, Philadelphia, PA, 2008.
- M. Hochbruck and C. Lubich, On Krylov subspace approximations to the matrix exponential operator, SIAM J. Numer. Anal. 34 (1997), pp. 1911–1925. doi: 10.1137/S0036142995280572
- S. Jaffard, Propriétés des matrices ⟨⟨bien localisées⟩⟩ près de leur diagonale et quelques applications, in Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Vol. 7. Elsevier, 1990, pp. 461–476.
- C. Kenney and A.J. Laub, Padé error estimates for the logarithm of a matrix, Int. J. Control. 50 (1989), pp. 707–730. doi: 10.1080/00207178908953392
- L. Knizhnerman and V. Simoncini, A new investigation of the extended Krylov subspace method for matrix function evaluations, Numer. Linear Algebra Appl. 17 (2010), pp. 615–638.
- L. Lopez and V. Simoncini, Analysis of projection methods for rational function approximation to the matrix exponential, SIAM J. Numer. Anal. 44 (2006), pp. 613–635. (electronic) doi: 10.1137/05062590
- Y.Y. Lu, Computing the logarithm of a symmetric positive definite matrix, Appl. Numer. Math. 26 (1998), pp. 483–496. doi: 10.1016/S0168-9274(97)00103-7
- G. Meurant, A review on the inverse of symmetric tridiagonal and block tridiagonal matrices, SIAM J. Matrix Anal. Appl. 13 (1992), pp. 707–728. doi: 10.1137/0613045
- C. Moler and C. Van Loan, Nineteen Dubious ways to compute the exponential of a matrix, twenty-five years later, SIAM Rev. 45 (2003), pp. 3–49. doi: 10.1137/S00361445024180
- I. Moret, Rational Lanczos approximations to the matrix square root and related functions, Numer. Linear Algebra Appl. 16 (2009), pp. 431–445. doi: 10.1002/nla.625
- I. Moret and P. Novati, RD-rational approximations of the matrix exponential, BIT Numer. Math. 44 (2004), pp. 595–615. doi: 10.1023/B:BITN.0000046805.27551.3b
- I. Moret and M. Popolizio, The restarted shift-and-invert Krylov method for matrix functions, Numer. Linear Algebra Appl. 21 (2014), pp. 68–80. doi: 10.1002/nla.1862
- R. Nabben, Decay rates of the inverse of nonsymmetric tridiagonal and band matrices, SIAM J. Matrix Anal. Appl. 20 (1999), pp. 820–837. doi: 10.1137/S0895479897317259
- M. Popolizio and V. Simoncini, Acceleration techniques for approximating the matrix exponential, SIAM J. Matrix Anal. Appl. 30 (2008), pp. 657–683. doi: 10.1137/060672856
- Y. Saad, Analysis of some Krylov subspace approximations to the matrix exponential operator, SIAM J. Numer. Anal. 29 (1992), pp. 209–228. doi: 10.1137/0729014
- Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed., Society for Industrial and Applied Mathematics, Philadelphia, PA, 2003.
- B.N. Sheehan, Y. Saad and R.B. Sidje, Computing exp(−τA)b with Laguerre polynomials, Electron. Trans. Numer. Anal. 37 (2010), pp. 147–165.
- R.B. Sidje, Expokit: A software package for computing matrix exponentials, ACM Trans. Math. Softw. (TOMS) 24 (1998), pp. 130–156. doi: 10.1145/285861.285868
- W. Stewart, Marca: Markov chain analyzer, a software package for Markov modeling, Numer. Solution Markov Chains 8 (1991), pp. 37.
- J. van den Eshof and M. Hochbruck, Preconditioning Lanczos approximations to the matrix exponential, SIAM J. Sci. Comput. 27 (2006), pp. 1438–1457. doi: 10.1137/040605461
- A. van Duin, Scalable parallel preconditioning with the sparse approximate inverse of triangular systems, SIAM J. Matrix Anal. Appl. 20 (1999), pp. 987–1006. doi: 10.1137/S0895479897317788