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On Chebyshev‐type methods free from second derivative
Communications in Numerical Methods in Engineering, 2007AbstractIn 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, 1951Abstract 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, 2020zbMATH 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, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dingfang Li, Ping Liu, Jisheng Kou
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Strong Stability Preserving Second Derivative General Linear Methods
Journal of Scientific Computing, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Afsaneh Moradi, Javad Farzi, Ali Abdi
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Halley's method for operators with unbounded second derivative
Applied Numerical Mathematics, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ezquerro, J. A. +1 more
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Strong stability preserving second derivative multistep methods
Numerical AlgorithmszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pari Khakzad +3 more
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Methods Involving Second or Higher Derivatives
2013Abstract 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, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Modified Chebyshev–Halley methods free from second derivative
Applied Mathematics and Computation, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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