Simplification and Accurate Implementation of State Evolution Recursion for Conjugate Gradient
Summary :
This letter simplifies and analyze existing state evolution recursions for conjugate gradient. The proposed simplification reduces the complexity for solving the recursions from cubic order to square order in the total number of iterations. The simplified recursions are still catastrophically sensitive to numerical errors, so that arbitrary-precision arithmetic is used for accurate evaluation of the recursions.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E106-A No.6 pp.952-956
- Publication Date
- 2023/06/01
- Publicized
- 2022/12/15
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2022EAL2088
- Type of Manuscript
- LETTER
- Category
- Communication Theory and Signals
Authors
Sakyo HASHIMOTO
Toyohashi University of Technology
Keigo TAKEUCHI
Toyohashi University of Technology
Keyword
Latest Issue
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Sakyo HASHIMOTO, Keigo TAKEUCHI, "Simplification and Accurate Implementation of State Evolution Recursion for Conjugate Gradient" in IEICE TRANSACTIONS on Fundamentals,
vol. E106-A, no. 6, pp. 952-956, June 2023, doi: 10.1587/transfun.2022EAL2088.
Abstract: This letter simplifies and analyze existing state evolution recursions for conjugate gradient. The proposed simplification reduces the complexity for solving the recursions from cubic order to square order in the total number of iterations. The simplified recursions are still catastrophically sensitive to numerical errors, so that arbitrary-precision arithmetic is used for accurate evaluation of the recursions.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2022EAL2088/_p
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@ARTICLE{e106-a_6_952,
author={Sakyo HASHIMOTO, Keigo TAKEUCHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Simplification and Accurate Implementation of State Evolution Recursion for Conjugate Gradient},
year={2023},
volume={E106-A},
number={6},
pages={952-956},
abstract={This letter simplifies and analyze existing state evolution recursions for conjugate gradient. The proposed simplification reduces the complexity for solving the recursions from cubic order to square order in the total number of iterations. The simplified recursions are still catastrophically sensitive to numerical errors, so that arbitrary-precision arithmetic is used for accurate evaluation of the recursions.},
keywords={},
doi={10.1587/transfun.2022EAL2088},
ISSN={1745-1337},
month={June},}
Copy
TY - JOUR
TI - Simplification and Accurate Implementation of State Evolution Recursion for Conjugate Gradient
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 952
EP - 956
AU - Sakyo HASHIMOTO
AU - Keigo TAKEUCHI
PY - 2023
DO - 10.1587/transfun.2022EAL2088
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E106-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2023
AB - This letter simplifies and analyze existing state evolution recursions for conjugate gradient. The proposed simplification reduces the complexity for solving the recursions from cubic order to square order in the total number of iterations. The simplified recursions are still catastrophically sensitive to numerical errors, so that arbitrary-precision arithmetic is used for accurate evaluation of the recursions.
ER -
English
