• Kyungpook Mathematical Journal
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• v.52 no.3
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• pp.347-357
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• 2012

When Newton's method, or Halley's method is used to approximate the pth root of 1-z, a sequence of rational functions is obtained. In this paper, a beautiful formula for these rational functions is proved in the square root case, using an interesting link to Chebyshev's polynomials. It allows the determination of the sign of the coefficients of the power series expansion of these rational functions. This answers positively the square root case of a proposed conjecture by Guo(2010).

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.527-538
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• 2000

We provide sufficient conditions for the monotone convergence of a Chebysheff-Halley-type method or method of tangent hyperbolas in a partially ordered topological space setting. The famous kantorovich theorem on fixed points is used here.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.1
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• pp.11-21
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• 2007

Given a nonlinear function f : $\mathbb{R}{\rightarrow}\mathbb{R}$ that has a simple real zero ${\alpha}$, a new numerical method to be called k-fold pseudo- Halley's method is proposed and it's error analysis is under investigation to confirm the convergence behavior near ${\alpha}$. Under the assumption that f is sufficiently smooth in a small neighborhood of ${\alpha}$, the order of convergence is found to be at least k+3. In addition, the corresponding asymptotic error constant is explicitly expressed in terms of k, ${\alpha}$ and f as well as the derivatives of f. A zero-finding algorithm is written and has been successfully implemented for numerous examples with Mathematica.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.83-108
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• 1997

Chebysheff-Halley methods are probably the best known cubically convergent iterative procedures for solving nonlinear equa-tions. These methods however require an evaluation of the second Frechet-derivative at each step which means a number of function eval-uations proportional to the cube of the dimension of the space. To re-duce the computational cost we replace the second Frechet derivative with a fixed bounded bilinear operator. Using the majorant method and Newton-Kantorovich type hypotheses we provide sufficient condi-tions for the convergence of our method to a locally unique solution of a nonlinear equation in Banach space. Our method is shown to be faster than Newton's method under the same computational cost. Finally we apply our results to solve nonlinear integral equations appearing in radiative transfer in connection with the problem of determination of the angular distribution of the radiant-flux emerging from a plane radiation field.

• Publications of The Korean Astronomical Society
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• v.22 no.4
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• pp.151-168
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• 2007

We have analyzed the comet records in the Korean history books: Samguksagi, Goryeosa, and Joseonwangjosillok. For a comparison, the Chinese and Japanese comet records collected by Kronk (1999) have also been analyzed. Power spectrum of the time series of the comet records is used to find periodic comets. Statistically significant periodicities in the power spectrum are detected at the periods of 38-40 years, about 76 years, and 300-400 years for all Korean, Chinese, and Japanese comet records. We have also calculated the past orbits of some comets that have been recently observed, to check whether or not they were recorded in the history books. We use a multistep method to numerically integrate the comet's orbital motion backward in time to 51 B.C. The gravitational force due to the Sun and the nine planets, non-gravitational force, and the relativistic effects have been considered. Comparison of comet's perihelion passage time and the position on the sky with the historical records shows that the comet Halley were recorded at every passage in both Goryeo and Joseon periods. The orbital motion of the comet Pons-Brooks has also been compared with the Korean records. For the comet Tempel-Tuttle, Swift-Tuttle, and Ikeya-Zhang, we have compared our calculation of the orbital motions with those of the previous studies.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.447-456
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• 1997

In this paper an accurate algorithm for the method of successive approximations for near-parabolic orbits is established symbolically. Numerical applications are given for motion predictions at fifteen epochs between the years 66 to 1835 for Halley's comet. and at fifteen epochs between the years 1417 to 1782 for Encke's comet. Comparisons with the standard Gauss method [4] show that the present algorithm is very accurate and efficient for motion pred-ications of near-parabolic orbits.

• Fisheries and Aquatic Sciences
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• v.21 no.11
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• pp.32.1-32.7
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• 2018

Trout production is a growing activity in recent years but requires new alternative sources of feed to be sustainable over time. The objective of this research was to determine the apparent digestibility coefficient (ADC) of dry matter (DM), organic matter (OM), crude protein (CP) and digestible energy (DE) of $ka{\tilde{n}}iwa$ (Chenopodium pallidicaule Aellen), kiwicha (Amaranthus caudatus L), quinoa (Chenopodium quinoa Willd), beans (Phaseolus vulgaris L.), sacha inchi, (Plukenetia volubilis L) and jumbo squid (Dosidicus gigas) meal in juvenile rainbow trout. The experimental diets were composed of a 70% basal diet and 30% of any raw materials. The ADC was determined by the indirect method using insoluble ash as a non-digestible marker. Jumbo squid, sacha inchi and quinoa showed the highest values of ADC (%) of DM (84.5, 73.5 and 69.7), OM (89.1, 78.4 and 72.9), CP (93.2, 98.0 and 90.3), and DE (4.57, 4.15 and 2.95 Mcal/kg DM), respectively. The ADC values for $ka{\tilde{n}}iwa$, kiwicha and bean were significantly lower. In conclusion, quinoa meal and jumbo squid meal have an acceptable digestibility but sacha inchi meal is a potential alternative for rainbow trout feeding in the future.