IGMRES method for linear systems

[1] Carden R. & Embree M. (2012) Ritz value localization for non-Hermitian matrices, SIAM Journal Matrix Analysis and its Applications, 33, 1320-1338. https://doi.org/10.1137/120872693

[2] Campbell, S. L., & Meyer, C. D. (2009). Generalized inverses of linear transformations. Society for industrial and applied Mathematics.

[3] Eiermann, M., Marek, I., & Niethammer, W. (1988). On the solution of singular linear systems of algebraic equations by semiiterative methods. Numerische Mathematik, 53(3), 265-283. https://doi.org/10.1007/BF01404464

[4] Freund, R. W., & Hochbruck, M. (1994). On the use of two QMR algorithms for solving singular systems and applications in Markov chain modeling. Numerical linear algebra with applications, 1(4), 403-420. https://doi.org/10.1002/nla.1680010406

[5] Goossens S. & Roose D. (1999) Ritz and harmonic Ritz values and the convergence of FOM and GMRES, Numerical Linear Algebra and its Applications, 6, 281-293. https://doi.org/10.1002/(SICI)1099-1506(199906)6:4<281::AID-NLA158>3.0.CO;2-B

[6] Greenbaum A. & Kyanfar F. & Salemi A. (2018) On the convergence rate of DGMRES, Linear Algebra and its Applications 552, 219-238. https://doi.org/10.1016/j.laa.2018.04.027

[7] Horn R. & Johnson C. (2013) Matrix Analysis, second edition, Cambridge.

[8] Ipsen I.C.F. & Meyer C.D. (1998) The idea behind Krylov methods, Amer. Math. Monthly, 105, 889-899. https://doi.org/10.1080/00029890.1998.12004985

[9] Kyanfar F. (2022) On stagnation of the DGMRES method, Iranian Journal of Numerical Analysis and Optimization, Vol 12. no.3, 533-541. https://doi.org/10.22067/IJNAO.2022.73913.1081

[10] Levine, J., & Hartwig, R. E. (1980). Applications of the Drazin Inverse to the Hill Cryptographic System. Part I. Cryptologia, 4(2), 71-85. https://doi.org/10.1080/0161-118091854906

[11] Liesen J. & Tichy P. (2009) On best approximation of polynomials in matrices in the matrix 2-norm, SIAM Journal Matrix Analysis and its Applications, 31, 853-863. https://doi.org/10.1137/080728299

[12] Nevanlinna, O.(1993) Convergence of iterations for linear equations, Lectures in Mathematics ETH Zurich. Basel: Birkhauser Verlag.

[13] Saad Y. & Schultz M.H. (1986;), GMRES: A generalized minimal residual algorithm for solving non symmetric linear systems, SIAM J. Sci. Statist. Comput., 7, 856-869. https://doi.org/10.1137/0907058

[14] Safarzadeh M. & Salemi A. (2018) DGMRES and index numerical range of matrices, Journal of Computational and Applied Mathematics, 335, 349-360. https://doi.org/10.1016/j.cam.2017.12.009

[15] Sidi A. (2001) DGMRES: A GMRES-type algorithm for Drazin-inverse solution of singular non symmetric linear systems, Linear Algebra and its Applications, 335, 189-204. https://doi.org/10.1016/S0024-3795(01)00289-0

[16] Simeon, B., Fuhrer, C., & Rentrop, P. (1993). The Drazin inverse in multibody system dynamics. Numerische Mathematik, 64, 521-539. https://doi.org/10.1007/BF01388703

[17] Toh K.C. (1996) Matrix approximation problems and nonsymmetric iterative methods, PhD dissertation, Cornell University, Ithaca, NY.