The performance of the interval midpoint zoro symmetric single-step (IMZSS2-5D) procedure to converge simultaneously to the zeros

Jamaludin, Noraini; Monsi, Mansor; Hassan, Nasruddin

doi:10.1063/1.5054232

Cited by 1 publication

(2 citation statements)

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“…We analyze the efficiency of the proposed method by comparing the computational results of the 52 test problems with the interval single-steps (IS2) method and its variants regarding the number of iterations and the largest final width of the interval generated [26,30,32]. The selected test examples are arranged starting from a real polynomial p(x) with degree n = 3 up to n = 12.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Later, Salim et al collaborated the idea of [20,21] and [24] by proving that the new extension approach known as the interval single-step (ISS2) method [25], has a superior order of convergence (R = 9) and lesser iterations generated. In 2018, Jamaludin et al [26] showed a significant reduction in the computational time when compared to its prior modifications, somehow; the R-order of convergence was not clear and has not been discussed by the authors.…”

Section: Introductionmentioning

confidence: 99%

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Improving the Convergence of Interval Single-Step Method for Simultaneous Approximation of Polynomial Zeros

et al. 2021

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This paper describes the extended method of solving real polynomial zeros problems using the single-step method, namely, the interval trio midpoint symmetric single-step (ITMSS) method, which updates the midpoint at each forward-backward-forward step. The proposed algorithm will constantly update the value of the midpoint of each interval of the previous roots before entering the preceding steps; hence, it always generate intervals that decrease toward the polynomial zeros. Theoretically, the proposed method possesses a superior rate of convergence at 16, while the existing methods are known to have, at most, 9. To validate its efficiency, we perform numerical experiments on 52 polynomials, and the results are presented, using performance profiles. The numerical results indicate that the proposed method surpasses the other three methods by fine-tuning the midpoint, which reduces the final interval width upon convergence with fewer iterations.

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Section: Numerical Experimentsmentioning

confidence: 99%