Bergamaschi, L., & Putti, M. (1999). Mixed finite elements and Newton-type linearizations for the solution of Richards’ equation. International Journal for Numerical Methods in Engineering, 45(8), 1025-1046. doi:10.1002/(sici)1097-0207(19990720)45:8<1025::aid-nme615>3.0.co;2-g
Notay, Y. (2001). Combination of Jacobi-Davidson and conjugate gradients for the partial symmetric eigenproblem. Numerical Linear Algebra with Applications, 9(1), 21-44. doi:10.1002/nla.246
Bergamaschi, L., & Martínez, A. (2014). Efficiently preconditioned inexact Newton methods for large symmetric eigenvalue problems. Optimization Methods and Software, 30(2), 301-322. doi:10.1080/10556788.2014.908878
[+]
Bergamaschi, L., & Putti, M. (1999). Mixed finite elements and Newton-type linearizations for the solution of Richards’ equation. International Journal for Numerical Methods in Engineering, 45(8), 1025-1046. doi:10.1002/(sici)1097-0207(19990720)45:8<1025::aid-nme615>3.0.co;2-g
Notay, Y. (2001). Combination of Jacobi-Davidson and conjugate gradients for the partial symmetric eigenproblem. Numerical Linear Algebra with Applications, 9(1), 21-44. doi:10.1002/nla.246
Bergamaschi, L., & Martínez, A. (2014). Efficiently preconditioned inexact Newton methods for large symmetric eigenvalue problems. Optimization Methods and Software, 30(2), 301-322. doi:10.1080/10556788.2014.908878
Bergamaschi, L., & Martínez, A. (2013). Parallel RFSAI-BFGS Preconditioners for Large Symmetric Eigenproblems. Journal of Applied Mathematics, 2013, 1-10. doi:10.1155/2013/767042
Martinez, J. M. (1993). A Theory of Secant Preconditioners. Mathematics of Computation, 60(202), 681. doi:10.2307/2153109
Morales, J. L., & Nocedal, J. (2000). Automatic Preconditioning by Limited Memory Quasi-Newton Updating. SIAM Journal on Optimization, 10(4), 1079-1096. doi:10.1137/s1052623497327854
Nabben, R., & Vuik, C. (2006). A Comparison of Deflation and the Balancing Preconditioner. SIAM Journal on Scientific Computing, 27(5), 1742-1759. doi:10.1137/040608246
Freitag, M. A., & Spence, A. (2007). A tuned preconditioner for inexact inverse iteration applied to Hermitian eigenvalue problems. IMA Journal of Numerical Analysis, 28(3), 522-551. doi:10.1093/imanum/drm036
Martínez, Á. (2016). Tuned preconditioners for the eigensolution of large SPD matrices arising in engineering problems. Numerical Linear Algebra with Applications, 23(3), 427-443. doi:10.1002/nla.2032
Gratton, S., Sartenaer, A., & Tshimanga, J. (2011). On A Class of Limited Memory Preconditioners For Large Scale Linear Systems With Multiple Right-Hand Sides. SIAM Journal on Optimization, 21(3), 912-935. doi:10.1137/08074008
Bergamaschi, L., Bru, R., & Martínez, A. (2011). Low-rank update of preconditioners for the inexact Newton method with SPD Jacobian. Mathematical and Computer Modelling, 54(7-8), 1863-1873. doi:10.1016/j.mcm.2010.11.064
DeGuchy, O., Erway, J. B., & Marcia, R. F. (2018). Compact representation of the full Broyden class of quasi‐Newton updates. Numerical Linear Algebra with Applications, 25(5). doi:10.1002/nla.2186
Nocedal, J., & Wright, S. J. (Eds.). (1999). Numerical Optimization. Springer Series in Operations Research and Financial Engineering. doi:10.1007/b98874
Dembo, R. S., Eisenstat, S. C., & Steihaug, T. (1982). Inexact Newton Methods. SIAM Journal on Numerical Analysis, 19(2), 400-408. doi:10.1137/0719025
Kelley, C. T. (1999). Iterative Methods for Optimization. doi:10.1137/1.9781611970920
Byrd, R. H., Nocedal, J., & Schnabel, R. B. (1994). Representations of quasi-Newton matrices and their use in limited memory methods. Mathematical Programming, 63(1-3), 129-156. doi:10.1007/bf01582063
Bergamaschi, L. (2020). A Survey of Low-Rank Updates of Preconditioners for Sequences of Symmetric Linear Systems. Algorithms, 13(4), 100. doi:10.3390/a13040100
Powers, R. T., & Størmer, E. (1970). Free states of the canonical anticommutation relations. Communications in Mathematical Physics, 16(1), 1-33. doi:10.1007/bf01645492
Ipsen, I. C. F., & Nadler, B. (2009). Refined Perturbation Bounds for Eigenvalues of Hermitian and Non-Hermitian Matrices. SIAM Journal on Matrix Analysis and Applications, 31(1), 40-53. doi:10.1137/070682745
Simoncini, V., & Eldén, L. (2002). Bit Numerical Mathematics, 42(1), 159-182. doi:10.1023/a:1021930421106
G. Sleijpen, G. L., & Van der Vorst, H. A. (1996). A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems. SIAM Journal on Matrix Analysis and Applications, 17(2), 401-425. doi:10.1137/s0895479894270427
Tapia, R. A., Dennis, J. E., & Schäfermeyer, J. P. (2018). Inverse, Shifted Inverse, and Rayleigh Quotient Iteration as Newton’s Method. SIAM Review, 60(1), 3-55. doi:10.1137/15m1049956
[-]