Modification of False-Position Method to Improve Its Convergence
Küçük Resim Yok
Tarih
2024
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Institute of Electrical and Electronics Engineers Inc.
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Root finding of polynomials is necessary for many engineering applications. Analytical root-finding methods may not be applicable when the orders of the polynomials are high or the objective function has fractional orders. In the literature many complex numerical root finding algorithms exist but they are not suitable for undergraduate courses. In this study a drawback of the False-Position method which occurs when the magnitudes of the function values at boundary points are disproportionate is eliminated. The highest function value at the boundary point is divided by the number of iteration in which the corresponding side is unchanged. This small modification improved the convergence capability of the False-Position method without compromising its simplicity. The modified algorithm is tested on two case study problems and the modified False-Position algorithm provided better results than its original state. In addition to this, the algorithm provided better results than bisection and secant root-finding algorithms. However, the convergence rate of Newton-Raphson is still better than the modified False-Position algorithm. The modified False-Position algorithm can be implemented for engineering problems and undergraduate courses due to its simplicity and relatively fast convergence capability. © 2024 IEEE.
Açıklama
8th International Artificial Intelligence and Data Processing Symposium, IDAP 2024 -- 21 September 2024 through 22 September 2024 -- Malatya -- 203423
Anahtar Kelimeler
convergence, false-position method, numerical analysis, root finding
Kaynak
8th International Artificial Intelligence and Data Processing Symposium, IDAP 2024
WoS Q Değeri
Scopus Q Değeri
N/A
