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Volume 1, Issue 6
A Note on the GMRES Method for Linear Discrete Ill-Posed Problems

Nao Kuroiwa & Takashi Nodera

Adv. Appl. Math. Mech., 1 (2009), pp. 816-829.

Published online: 2009-01

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  • Abstract

In this paper, we are presenting a proposal for new modified algorithms for RRGMRES and AGMRES. It is known that RRGMRES and AGMRES are viable methods for solving linear discrete ill-posed problems. In this paper we have focused on the residual norm and have come up with two improvements where successive updates and the stabilization of decreases for the residual norm improve performance respectively. Our numerical experiments confirm that our improved algorithms are effective for linear discrete ill-posed problems.

  • Keywords

Numerical computation, GMRES, iterative method, linear discrete ill-posed problem.

  • AMS Subject Headings

65F10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-1-816, author = {Nao and Kuroiwa and and 20543 and and Nao Kuroiwa and Takashi and Nodera and and 20544 and and Takashi Nodera}, title = {A Note on the GMRES Method for Linear Discrete Ill-Posed Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2009}, volume = {1}, number = {6}, pages = {816--829}, abstract = {

In this paper, we are presenting a proposal for new modified algorithms for RRGMRES and AGMRES. It is known that RRGMRES and AGMRES are viable methods for solving linear discrete ill-posed problems. In this paper we have focused on the residual norm and have come up with two improvements where successive updates and the stabilization of decreases for the residual norm improve performance respectively. Our numerical experiments confirm that our improved algorithms are effective for linear discrete ill-posed problems.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.09-m09S08}, url = {http://global-sci.org/intro/article_detail/aamm/8399.html} }
TY - JOUR T1 - A Note on the GMRES Method for Linear Discrete Ill-Posed Problems AU - Kuroiwa , Nao AU - Nodera , Takashi JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 816 EP - 829 PY - 2009 DA - 2009/01 SN - 1 DO - http://doi.org/10.4208/aamm.09-m09S08 UR - https://global-sci.org/intro/article_detail/aamm/8399.html KW - Numerical computation, GMRES, iterative method, linear discrete ill-posed problem. AB -

In this paper, we are presenting a proposal for new modified algorithms for RRGMRES and AGMRES. It is known that RRGMRES and AGMRES are viable methods for solving linear discrete ill-posed problems. In this paper we have focused on the residual norm and have come up with two improvements where successive updates and the stabilization of decreases for the residual norm improve performance respectively. Our numerical experiments confirm that our improved algorithms are effective for linear discrete ill-posed problems.

Nao Kuroiwa & Takashi Nodera. (1970). A Note on the GMRES Method for Linear Discrete Ill-Posed Problems. Advances in Applied Mathematics and Mechanics. 1 (6). 816-829. doi:10.4208/aamm.09-m09S08
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