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Journals / Konuralp Journal of Mathematics / 2014 / Cilt: 2 - Sayı: 2

KOCAK'S ACCELERATION METHOD SMOOTHLY GEARS UP ITERATIVE SOLVERS

Mehmet Çetin KOÇAK
Pages
109–119
Publication Date
2014-12-01
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Ko¸cak’s method gKaccelerates g by actually solving a superior secondary solver obtained from afixed-point preserving transformationg where G is a gain and m is the slope of a straight line joining g and g = x= x + G(g − x) = (g − mx)/(1 − m), m = 1 − 1/G, G = 1/(1 − m)

📌 3 Key Takeaways

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Objective & Hypothesis:Consider a scalar repetitive scheme symbolically represented byxk+1= g(xk) where k is the iteration count.
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Key Findings & Data:Let z and n respectively denote the target fixed-point and convergence order of g.
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Conclusion & Impact:Ko¸cak’s method gKaccelerates g by actually solving a superior secondary solver obtained from afixed-point preserving transformationg where G is a gain and m is the slope of a straight line joining g and g = x= x + G(g − x) = (g − mx)/(1 − m), m = 1 − 1/G, G = 1/(1 − m)
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Non-linear equations · Iterative methods · Newton’s method

Abstract

Consider a scalar repetitive scheme symbolically represented byxk+1= g(xk) where k is the iteration count. Let z and n respectively denote the target fixed-point and convergence order of g. Ko¸cak’s method gKaccelerates g by actually solving a superior secondary solver obtained from afixed-point preserving transformationg where G is a gain and m is the slope of a straight line joining g and g = x= x + G(g − x) = (g − mx)/(1 − m), m = 1 − 1/G, G = 1/(1 − m)

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Cite This Article

KOÇAK, M. Ç. (2014). KOCAK'S ACCELERATION METHOD SMOOTHLY GEARS UP ITERATIVE SOLVERS. Konuralp Journal of Mathematics, Cilt: 2 - Sayı: 2, 109–119. https://ajindex.com/articles/786764

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References (3)

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