References
- S. Bellavia, and S. Berrone (2007). Globalization strategies for Newton–Krylov methods for stabilized FEM discretization of Navier–Stokes equations. J. Comput. Phys., 226, 2317–2340. (doi:10.1016/j.jcp.2007.07.021) doi: 10.1016/j.jcp.2007.07.021
- S. Bellavia, D. Bertaccini, and B. Morini (2011). Nonsymmetric preconditioner updates in Newton–Krylov methods for nonlinear systems. SIAM J. Sci. Comput., 33, 2595–2619. (doi:10.1137/100789786) doi: 10.1137/100789786
- S. Bellavia, C. Cartis, N. I.M. Gould, B. Morini, and Ph. L. Toint (2010). Convergence of a regularized Euclidean residual algorithm for nonlinear least-squares. SIAM J. Numer. Anal., 48, 1–29. (doi:10.1137/080732432) doi: 10.1137/080732432
- S. Bellavia, V. De Simone, D. di Serafino, and B. Morini (2011). Efficient preconditioner updates for shifted linear systems. SIAM J. Sci. Comput., 33, 1785–1809. (doi:10.1137/100803419) doi: 10.1137/100803419
- S. Bellavia, V. De Simone, D. di Serafino, and B. Morini (2012). A preconditioning framework for sequences of diagonally modified linear systems arising in optimization. SIAM J. Numer. Anal., 50, 3280–3302. (doi:10.1137/110860707) doi: 10.1137/110860707
- S. Bellavia, and B. Morini (2001). A globally convergent Newton-GMRES subspace method for systems of nonlinear equations. SIAM J. Sci. Comput., 23, 940–960. (doi:10.1137/S1064827599363976) doi: 10.1137/S1064827599363976
- S. Bellavia, and B. Morini (2006). Subspace trust-region methods for large bound-constrained nonlinear equations. SIAM J. Numer. Anal., 44, 1535–1555. (doi:10.1137/040611951) doi: 10.1137/040611951
- M. Benzi, and G. H. Golub (1999). Bounds of the entries of matrix functions with applications to preconditioning. BIT, 39, 417–438. (doi:10.1023/A:1022362401426) doi: 10.1023/A:1022362401426
- M. Benzi, and M. Tu˙ma (1998). A sparse approximate inverse preconditioner for nonsymmetric linear systems. SIAM J. Sci. Comput., 19, 968–994. (doi:10.1137/S1064827595294691) doi: 10.1137/S1064827595294691
- M. Benzi, and M. Tu˙ma (1999). A comparative study of sparse approximate inverse preconditioners. Appl. Numer. Math., 30, 305–340. (doi:10.1016/S0168-9274(98)00118-4) doi: 10.1016/S0168-9274(98)00118-4
- L. Bergamaschi, R. Bru, A. Martinez, and M. Putti (2006). Quasi-Newton preconditioners for the inexact Newton method. Electron. Trans. Numer. Anal., 23, 76–87.
- D. Bertaccini, and S. Filippone Sparse approximate inverse preconditioners revisited. , submitted for publication.
- P. Birken, J. Duintjer Tebbens, A. Meister, and M. Tuma (2008). Preconditioner updates applied to CFD model problems. Appl. Numer. Math., 58, 1628–1641. (doi:10.1016/j.apnum.2007.10.001) doi: 10.1016/j.apnum.2007.10.001
- P. N. Brown (1987). A local convergence theory for combined inexact-Newton/finite-difference projection methods. SIAM J. Numer. Anal., 24, 407–434. (doi:10.1137/0724031) doi: 10.1137/0724031
- P. N. Brown, and Y. Saad (1994). Convergence theory of nonlinear Newton–Krylov algorithms. SIAM J. Optim., 4, 297–330. (doi:10.1137/0804017) doi: 10.1137/0804017
- C. Calgaro, J. P. Chehab, and Y. Saad (2010). Incremental incomplete ILU factorizations with applications. Numer. Linear Algebra Appl., 17, 811–837. (doi:10.1002/nla.756) doi: 10.1002/nla.756
- S. Demko, W. F. Moss, and P. W. Smith (1984). Decay rates for inverses of band matrices. Math. Comput., 43, 491–499. (doi:10.1090/S0025-5718-1984-0758197-9) doi: 10.1090/S0025-5718-1984-0758197-9
- J. Duintjer Tebbens, and M. Tu˙ma (2007). Efficient preconditioning of sequences of nonsymmetric linear systems. SIAM J. Sci. Comput., 29, 1918–1941. (doi:10.1137/06066151X) doi: 10.1137/06066151X
- J. Duintjer Tebbens, and M. Tu˙ma (2010). Preconditioner updates for solving sequences of linear systems in matrix-free environment. Numer. Linear Algebra Appl., 17, 997–1019. (doi:10.1002/nla.695) doi: 10.1002/nla.695
- S. C. Eisenstat, and H. F. Walker (1994). Globally convergent inexact Newton methods. SIAM J. Optim., 4, 393–422. (doi:10.1137/0804022) doi: 10.1137/0804022
- C. A. Floudas, P. M. Pardalos, C. S. Adjiman, W. R. Esposito, Z. Gumus, S. T. Harding, J. L. Klepeis, C. A. Meyer, and C. A. Schweiger (1999). Handbook of Test Problems in Local and Global Optimization. Nonconvex Optimization and Its Applications, Dordrecht: Kluwer Academic Publishers.33
- N. I.M. Gould, M. Porcelli, and Ph. L. Toint (2011). Updating the regularization parameter in the adaptive cubic regularization algorithm. Comput. Optim. Appl., 53, 1–22. (doi:10.1007/s10589-011-9446-7) doi: 10.1007/s10589-011-9446-7
- M. Hinze, R. Pinnau, M. Ulbrich, and S. Ulbrich (2009). Optimization with PDE Constraints. Springer-Verlag New York Inc, Dordrecht:
- D. A. Knoll, and D. E. Keyes (2004). Jacobian-free Newton–Krylov methods, a survey of approaches and applications. J. Comput. Phys., 193, 357–397. (doi:10.1016/j.jcp.2003.08.010) doi: 10.1016/j.jcp.2003.08.010
- F. Lemeire (1975). Bounds for condition numbers of triangular and trapezoid matrices. BIT, 15, 58–64. (doi:10.1007/BF01932996) doi: 10.1007/BF01932996
- G. Meurant (1992). A review on the inverse of symmetric tridiagonal and block tridiagonal matrices. SIAM J. Matrix Anal. Appl., 13, 707–728. (doi:10.1137/0613045) doi: 10.1137/0613045
- R. Nabben (1999). Decay rates of the inverse of nonsymmetric tridiagonal and band matrices. SIAM J. Matrix Anal. Appl., 20, 820–837. (doi:10.1137/S0895479897317259) doi: 10.1137/S0895479897317259
- M. L. Parks, E. de Sturler, G. Mackey, D. D. Johnson, and S. Maiti (2006). Recycling Krylov subspaces for sequences of linear systems. SIAM J. Sci. Comput., 28, 1651–1674. (doi:10.1137/040607277) doi: 10.1137/040607277
- R. P. Pawlowski, J. N. Shadid, J. P. Simonis, and H. F. Walker (2006). Globalization techniques for Newton–Krylov methods and applications to the fully-coupled solution of the Navier–Stokes equations. SIAM Rev., 48, 700–721. (doi:10.1137/S0036144504443511) doi: 10.1137/S0036144504443511
- R. P. Pawlowski, J. N. Shadid, J. P. Simonis, and H. F. Walker (2008). Inexact Newton dogleg methods. SIAM J. Numer. Anal., 46, 2112–2132. (doi:10.1137/050632166) doi: 10.1137/050632166
- M. Pernice, and H. F. Walker (1998). NITSOL: A new iterative solver for nonlinear systems. SIAM J. Sci. Comput., 19, 302–318. (doi:10.1137/S1064827596303843) doi: 10.1137/S1064827596303843
- M. Porcelli (2013). On the convergence of an inexact Gauss–Newton trust-region method for nonlinear least-squares problems with simple bounds. Optim. Lett., 7, 447–465. (doi:10.1007/s11590-011-0430-z) doi: 10.1007/s11590-011-0430-z
- P. S. Vassilevski (1990). On some ways of approximating inverses of banded matrices in connection with deriving preconditioners based on incomplete block factorizations. Computing, 43, 277–296. (doi:10.1007/BF02242922) doi: 10.1007/BF02242922