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A Superquadratic Variant of Newton's Method
SIAM Journal on Numerical Analysis, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Multidimensional Interval Newton Method
Reliable Computing, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On an Aitken–Newton type method
Numerical Algorithms, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ion Pavaloiu, Emil Catinas
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1975
Many of the equations arising in practical problems are of a type difficult or impossible to solve by the standard algebraic methods. For example, the equations: $$ 2\sin {\kern 1pt} x - x = 0{\kern 1pt} {\kern 1pt} {e^x} - 2x - 1 = 0,{\kern 1pt} {\kern 1pt} {x^6} - 3x + 1 = 0 $$ have roots which we may estimate, by graphing the functions and ...
Brian Knight, Roger Adams
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Many of the equations arising in practical problems are of a type difficult or impossible to solve by the standard algebraic methods. For example, the equations: $$ 2\sin {\kern 1pt} x - x = 0{\kern 1pt} {\kern 1pt} {e^x} - 2x - 1 = 0,{\kern 1pt} {\kern 1pt} {x^6} - 3x + 1 = 0 $$ have roots which we may estimate, by graphing the functions and ...
Brian Knight, Roger Adams
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2019
Newton’s method was invented by Newton to solve the nonlinear one-dimensional problem. Later it was extended to solve multivariable nonlinear optimization problems. It is well known that the method of steepest descent uses only the first-order derivative (gradient).
Shashi Kant Mishra, Bhagwat Ram
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Newton’s method was invented by Newton to solve the nonlinear one-dimensional problem. Later it was extended to solve multivariable nonlinear optimization problems. It is well known that the method of steepest descent uses only the first-order derivative (gradient).
Shashi Kant Mishra, Bhagwat Ram
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Accelerated Convergence in Newton’s Method
SIAM Review, 1994\textit{G. H. Brown jun.} [Am. Math. Monthly 84, 726-728 (1977; Zbl 0375.65025)] and \textit{G. Alefeld} [ibid. 88, 530-536 (1981; Zbl 0486.65035)] applied Newton's method to \(F(x):= f(x)/\sqrt{f'(x)}\), \(f\) being a real-valued function of a real variable, to solve \(f(x)= 0\) approximately, and thus obtained Halley's method for \(f\).
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REPEATED PLAY AND NEWTON'S METHOD
International Game Theory Review, 2000Motivated by repeated play of non-cooperative games, we study equation solving undertaken in parallel by several non-communicating agents, each dealing with his own block of variables. The process is akin to Newton's method in using derivative information.
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A Classification of Quasi-Newton Methods
Numerical Algorithms, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Gauss–Newton Method: Least Squares, Relation to Newton’s Method
2001William R. Esposito +1 more
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