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Any non-decreasing sequence of non-negative numbers can be the convergence curve of the DGMRES method | ||
| Journal of New Researches in Mathematics | ||
| مقاله 12، دوره 7، شماره 32، بهمن و اسفند 2021، صفحه 165-176 اصل مقاله (437.71 K) | ||
| نوع مقاله: research paper | ||
| نویسندگان | ||
Malihe Safarzadeh1؛ Hossein Sadeghi Goughery  2
| ||
| 1Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran | ||
| 2Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran | ||
| چکیده | ||
| Investigating the convergence of the Krylov subspace methods has been considered as one of the favorite subjects in the field of numerical linear algebra. Given that the DGMRES method is a Krylov subspace methods, there is not much work to be done on its convergence. In this article we will discuss parts of the convergence of this method. We show that for any non-decreasing sequence of negative numbers f(0)≥f(1)≥⋯≥f(m-1)>f(m)=⋯=f(n)=0, he set of {λ_1,…,λ_m,0,…,0} of the complex numbers and the arbitrary number α≤n-m can be a set of singular linear equations n×n, Ax=b with the index α and the set {λ_1,…,λ_m,0,…,0} as the spectrum of matrix A such that if the DGMRES method is used to solve this system, assuming ‖A^α r_0 ‖_2=f(0)‖_2 = f (0), for k=1,…,m-1, the k^th residual vector is ‖A^α 〖r 〗_k ‖_2=f(k), wherer_0=b-Ax_0 is the initial residual vector. We attempt to do this by constructing the complete coefficient matrix of the system (s). | ||
| کلیدواژهها | ||
| Singular linear system؛ - index- Drazin؛ inverse-residual vector | ||
| مراجع | ||
|
[1]
|
S. Campbell and C. J. Meyer, Generalized Inverses of Linear Transformations, Pitman, London, San Francisco, Melbourne, 1979.
|
|
|
[2]
|
Y. Saad, "Krylov subspace methods for solving large unsymmetric linear systems," Mathematics of Computation, vol. 37, pp. 105-126, 1981.
|
|
|
[3]
|
Y. Saad and M. H. Schultz, "GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems," SIAM Journal on Scientific and Statistical Computing, vol. 7, p. 856–869, 1986.
|
|
|
[4]
|
A. Sidi, "DGMRES: A GMRES-type algorithm for Drazin-inverse solution of singular nonsymmetric linear systems," Linear Algebra and its Applications, vol. 335, p. 189–204, 2001.
|
|
|
[5]
|
J. Liesen and Z. Strakos, "Convergence of GMRES for Tridiagonal Toeplitz Matrices," SIAM Journal on Matrix Analysis and Applications, vol. 26, no. 1, p. 233–251, 2004.
|
|
|
[6]
|
J. Liesen and P. Tichý, "The worst-case GMRES for normal matrices," BIT Numerical mathematics, vol. 44, no. 1, pp. 79-98, 2004.
|
|
|
[7]
|
J. Liesen and Z. Strakos, "GMRES Convergence Analysis for a Convection-Diffusion Model Problem," SIAM Journal on Scientific Computing, vol. 26, no. 6, pp. 1989-2009, 2005.
|
|
|
[8]
|
R. C. Li and W. Zhang, "The rate of convergence of GMRES on a tridiagonal toeplitz linear system. II," Linear Algebra and its Applications, vol. 431, no. 12, pp. 2425-2436, 2009.
|
|
|
[9]
|
A. Greenbaum, F. Kyanfar and A. Salemi, "On the convergence rate of DGMRES," Linear Algebra and its Applications, vol. 552, pp. 219-238, 2018.
|
|
|
[10]
|
M. Safarzadeh and A. Salemi, "DGMRES and index numerical range of matrices," Journal of Computational and Applied Mathematics, vol. 335, pp. 349-360, 2018.
|
|
|
[11]
|
A. Greenbaum, V. Pták and Z. Strakoš, "Any Nonincreasing Convergence Curve is Possible for GMRES," SIAM Journal on Matrix Analysis and Applications, vol. 17, no. 3, p. 465–469, 1996.
|
|
|
[12]
|
Y. Saad, Iterative Methods for Sparse Linear Systems, Philadelphia: SIAM, 2003.
|
|
|
[13]
|
J. J. Climent, M. Neumann and A. Sidi, "A semi-iterative method for singular linear systems with arbitrary index," Journal of Computational and Applied Mathematics, vol. 87, no. 1, pp. 21-38, 1997.
|
|
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