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On Chebyshev‐type methods free from second derivative

Communications in Numerical Methods in Engineering, 2007
AbstractIn this paper, we present a new Chebyshev‐type method free from second derivative. An analysis of convergence shows that the new method has fourth‐order convergence. Per iteration, the method requires one evaluation of the function and two of its first derivative and therefore this method has the efficiency index equal to 1.587.
Kou, Jisheng, Li, Yitian
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The second derivative method of gravity interpretation

Geophysics, 1951
Abstract The second derivative method of interpreting gravity data, although its use is justifiable only on data of high accuracy, offers a simple routine method of locating some types of geologic anomalies of importance in oil and mineral reconnaissance. The theoretical formula by which it is possible to compute the second (vertical)
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Implementation of second derivative general linear methods

Calcolo, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abdi Ali, Conte Dajana
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An improvement of Chebyshev–Halley methods free from second derivative

Applied Mathematics and Computation, 2014
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Dingfang Li, Ping Liu, Jisheng Kou
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Strong Stability Preserving Second Derivative General Linear Methods

Journal of Scientific Computing, 2019
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Afsaneh Moradi, Javad Farzi, Ali Abdi
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Halley's method for operators with unbounded second derivative

Applied Numerical Mathematics, 2007
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Ezquerro, J. A.   +1 more
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Strong stability preserving second derivative multistep methods

Numerical Algorithms
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Pari Khakzad   +3 more
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Methods Involving Second or Higher Derivatives

2013
Abstract Whereas Newton’s method involves only the first derivative, methods discussed in this chapter involve the second or higher. The “classical” methods of this type (such as Halley’s, Euler’s, Hansen and Patrick’s, Ostrowski’s, Cauchy’s and Chebyshev’s) are all third order with three evaluations, so are slightly more efficient than Newton’s ...
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Some second-derivative-free variants of Chebyshev–Halley methods

Applied Mathematics and Computation, 2007
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Modified Chebyshev–Halley methods free from second derivative

Applied Mathematics and Computation, 2008
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