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Paper Abstract and Keywords
Presentation 2025-12-11 16:20
Performance Evaluation of Residual-Convergent ODEs for Fixed-Point Search
Yuu Miino (Naruto Univ. Edu.) NLP2025-68
Abstract (in Japanese) (See Japanese page) 
(in English) In this study, we evaluate the performance of a method for finding fixed points of discrete-time dynamical systems using residual-convergent ordinary differential equations (ODEs). Numerical experiments reveal changes in computation time, step size, and function evaluation count with respect to the residual convergence parameter gamma, indicating that appropriate selection of gamma affects computational effciency. By visualizing the computation stopping regions and gradients of the residuals in the state space, we elucidate the relationship between extremal points of the residuals and convergence properties. Additionally, we demonstrate that trajectories converging to (or diverging from) extremal points halt their calculations, elucidating the underlying mechanism and showing that residual-convergent ODEs exhibit properties similar to gradient methods. From these results, we conclude that while residual-convergent ODEs are effective for fixed-point searches, they are subject to similar constraints as gradient methods.
Keyword (in Japanese) (See Japanese page) 
(in English) Fixed Point / Ordinary Differential Equation / Numerical Computation / Asymptotic Stability / / / /  
Reference Info. IEICE Tech. Rep., vol. 125, no. 283, NLP2025-68, pp. 78-81, Dec. 2025.
Paper # NLP2025-68 
Date of Issue 2025-12-04 (NLP) 
ISSN Online edition: ISSN 2432-6380
Copyright
and
reproduction		 All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
Download PDF NLP2025-68

Conference Information
Committee NLP  
Conference Date 2025-12-11 - 2025-12-12 
Place (in Japanese) (See Japanese page) 
Place (in English) Kochi Castle Museum of History 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Nonlinear problem, etc 
Paper Information
Registration To NLP 
Conference Code 2025-12-NLP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Performance Evaluation of Residual-Convergent ODEs for Fixed-Point Search 
Sub Title (in English)  
Keyword(1) Fixed Point  
Keyword(2) Ordinary Differential Equation  
Keyword(3) Numerical Computation  
Keyword(4) Asymptotic Stability  
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1st Author's Name Yuu Miino  
1st Author's Affiliation Naruto University of Education (Naruto Univ. Edu.)
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Speaker Author-1 
Date Time 2025-12-11 16:20:00 
Presentation Time 20 minutes 
Registration for NLP 
Paper # NLP2025-68 
Volume (vol) vol.125 
Number (no) no.283 
Page pp.78-81 
#Pages 4 
Date of Issue 2025-12-04 (NLP) 

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