PERFORMANCE COMPARISON OF FIXED-POINT ITERATION METHOD AND TEACHING-LEARNING BASED OPTIMISATION: A STUDY ON NONLINEAR EQUATION SYSTEMS
Öz
Bu çalışma iki ana hedefe odaklanmaktadır. İlk olarak, matematiksel tabanlı sabit nokta iterasyon yöntemi ile metasezgisel öğretme-öğrenme tabanlı optimizasyon yöntemi arasındaki benzerlikler ve farklılıklar sunulmuştur. İkinci olarak, bu iki yöntemin karmaşık bir doğrusal denklem sisteminin çözümünü bulmadaki performansı karşılaştırılmaktadır. Bu sayede diğer araştırmacılar, daha önce yazarlar tarafından sırasıyla [2] ve [3]'te tartışılan sonuçlar arasında bir karşılaştırma yapabilecek ve gelecekteki araştırmalarında bu sonuçları kullanarak gerekli optimizasyon yöntemini seçme konusunda fikir sahibi olabileceklerdir.
Anahtar Kelimeler
root finding fixed point iteration method teaching learning based algorithm
Kaynakça
- R. P. Chapra, S.C. Canale, Numerical Methods for Engineers, McGraw-Hill Higher Education, New York, (2002).
- B. Köse, B. Demirtürk, and Ş. Konca, Finding Solutions of Nonlinear Equation Systems with Newton Raphson and Red Fox Methods, 6th International Graduate Studies Congress-IGSCONG 2024, June 5-8, 2024.
- B. Demirtürk, B. Köse, Ş. Konca, Finding the Solution of a System of Nonlinear Equations with Sine Cosine and Particle Swarm Optimization Algorithms, 6th International Istanbul Modern Scientific Research Congress, 5-7 July 2024, Istanbul, (2024).
- T. Gemechu, S. Thota, On New Root Finding Algorithm for Solving Nonlinear Transcendental Equations, International Journal of Chemistry, Mathematics and Physics (IJCMP), Vol.4, No.2, pp.18-24 (2020).
- T. Gemechu, Root finding for nonlinear equations, Mathematical Theory and Modeling, Vol.8, No.7, 10 pages, (2018).
- V. Y. Semenov, A Method to Find all the Roots of the System of Nonlinear Algebraic Equations Based on the Krawczyk Operator, Cybernetic and Systems Analysis, Vol.51, No.5, pp.819-825 (2015).
- J. M. Ortega, W. C. Rheinbolt, Iterative Solution of Nonlinear Equations in Several Variables; Academic Press: New York, NY, USA, (1970).
- C. T. Kelley, Iterative methods for linear and nonlinear equations, Society for Industrial and Applied Mathematics, (1995).
- J. F. Traub, Iterative Methods for the Solution of Equations; American Mathematical Soc.: Washington, WA, USA, (1982).
- C. G. Broyden, A class of methods for solving nonlinear simultaneous equations, Mathematics of Computation, Vol.19, pp.577-593 (1965).
- B. Köse, F. Kaya, Öğretme ve Öğrenme Tabanlı Optimizasyon, Teknobilim 2023: Optimizasyon Modelleme ve Yapay Zeka Optimizasyon Algoritmaları, Efe Akademi, İstanbul, (2023).
- R.V. Rao, V. J. Savsani and D. P. Vakharia, Teaching-Learning-Based Optimization: A Novel Method for Constrained Mechanical Design Optimization Problems. Computer-Aided Design, Vol.43, pp.303-315 (2011).
- K. Ömeroğlu, Lineer Olmayan Denklemler ve Geogebra Uygulamaları, Recep Tayyip Erdoğan Üniversitesi Fen Bilimleri Enstitüsü Yüksek Lisans Tezi, (2019).
Öz
Kaynakça
- R. P. Chapra, S.C. Canale, Numerical Methods for Engineers, McGraw-Hill Higher Education, New York, (2002).
- B. Köse, B. Demirtürk, and Ş. Konca, Finding Solutions of Nonlinear Equation Systems with Newton Raphson and Red Fox Methods, 6th International Graduate Studies Congress-IGSCONG 2024, June 5-8, 2024.
- B. Demirtürk, B. Köse, Ş. Konca, Finding the Solution of a System of Nonlinear Equations with Sine Cosine and Particle Swarm Optimization Algorithms, 6th International Istanbul Modern Scientific Research Congress, 5-7 July 2024, Istanbul, (2024).
- T. Gemechu, S. Thota, On New Root Finding Algorithm for Solving Nonlinear Transcendental Equations, International Journal of Chemistry, Mathematics and Physics (IJCMP), Vol.4, No.2, pp.18-24 (2020).
- T. Gemechu, Root finding for nonlinear equations, Mathematical Theory and Modeling, Vol.8, No.7, 10 pages, (2018).
- V. Y. Semenov, A Method to Find all the Roots of the System of Nonlinear Algebraic Equations Based on the Krawczyk Operator, Cybernetic and Systems Analysis, Vol.51, No.5, pp.819-825 (2015).
- J. M. Ortega, W. C. Rheinbolt, Iterative Solution of Nonlinear Equations in Several Variables; Academic Press: New York, NY, USA, (1970).
- C. T. Kelley, Iterative methods for linear and nonlinear equations, Society for Industrial and Applied Mathematics, (1995).
- J. F. Traub, Iterative Methods for the Solution of Equations; American Mathematical Soc.: Washington, WA, USA, (1982).
- C. G. Broyden, A class of methods for solving nonlinear simultaneous equations, Mathematics of Computation, Vol.19, pp.577-593 (1965).
- B. Köse, F. Kaya, Öğretme ve Öğrenme Tabanlı Optimizasyon, Teknobilim 2023: Optimizasyon Modelleme ve Yapay Zeka Optimizasyon Algoritmaları, Efe Akademi, İstanbul, (2023).
- R.V. Rao, V. J. Savsani and D. P. Vakharia, Teaching-Learning-Based Optimization: A Novel Method for Constrained Mechanical Design Optimization Problems. Computer-Aided Design, Vol.43, pp.303-315 (2011).
- K. Ömeroğlu, Lineer Olmayan Denklemler ve Geogebra Uygulamaları, Recep Tayyip Erdoğan Üniversitesi Fen Bilimleri Enstitüsü Yüksek Lisans Tezi, (2019).
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Temel Matematik (Diğer) |
| Bölüm | Teorik Makale |
| Yazarlar | |
| Gönderilme Tarihi | 17 Eylül 2024 |
| Kabul Tarihi | 2 Aralık 2024 |
| Yayımlanma Tarihi | 31 Ocak 2025 |
| DOI | https://doi.org/10.33773/jum.1551816 |
| IZ | https://izlik.org/JA69YJ35UE |
| Yayımlandığı Sayı | Yıl 2025 Cilt: 8 Sayı: 1 |