This paper aims to propose a constructive methodology for determining the matrix sign function for a stable variant of the Kung-Traub method. It analytically shows that the new scheme is asymptotically stable. Different numerical experiments compare the new scheme's beh More
This paper aims to propose a constructive methodology for determining the matrix sign function for a stable variant of the Kung-Traub method. It analytically shows that the new scheme is asymptotically stable. Different numerical experiments compare the new scheme's behavior with the existing matrix iteration of the same type. Finally, the given approach applies to solve the algebraic Riccati equation and the Sylvester equation.
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The primary goal of this work is to introduce two adaptive Steffensen-like methods with memory of the highest efficiency indices. In the existing methods, to improve the convergence order applied to memory concept, the focus has only been on the current and previous ite More
The primary goal of this work is to introduce two adaptive Steffensen-like methods with memory of the highest efficiency indices. In the existing methods, to improve the convergence order applied to memory concept, the focus has only been on the current and previous iteration. However, it is possible to improve the accelerators. Therefore, we achieve superior convergence orders and obtain as high efficiency indices as possible.
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In this paper, two adaptive methods with memory are improved based on Cordero- Torregrosa method. The technique of adaptive method increases the efficiency index as high as possible. The new derivative free methods have possessed the convergence order 7.46315 and 7.9931 More
In this paper, two adaptive methods with memory are improved based on Cordero- Torregrosa method. The technique of adaptive method increases the efficiency index as high as possible. The new derivative free methods have possessed the convergence order 7.46315 and 7.99315, and they only use the information from the last two iterations. Finally, we provide convergence analysis and numerical examples to illustrate the proposed methods.
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