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error bounds for newton's method

Optimal Error Bounds for the Newton–Kantorovich Theorem
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Best possible upper and lower bounds for the error in Newton's method are established under the hypotheses of the Kantorovich theorem.
Newton's Method Error Bound
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MAT 4310: 1. Newton's Method Error Bound. Theorem (Newton1–Raphson Method2 (1711)). Suppose f has 2 continuous derivatives on a neighborhood B of a root r.
Newton's method - Wikipedia
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The Newton–Fourier method is Joseph Fourier's extension of Newton's method to provide bounds on the absolute error of the root approximation, ...
Optimal Error Bounds for the Newton–Kantorovich Theorem ...
https://epubs.siam.org/doi/10.1137/0711002
14.07.2006 · (2013) Estimating upper bounds on the limit points of majorizing sequences for Newton’s method. Numerical Algorithms 62 :1, 115-132. (2012) Secant-type methods and nondiscrete induction.
Optimal Error Bounds for the Newton-Kantorovich Theorem
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Best possible upper and lower bounds for the error in Newton's method are established under the hypotheses of the Kantorovich theorem. Let X and Y be Banach ...
Topic 10.3: Newton's Method (Error Analysis)
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Given that we are using Newton's method to approximate a root of the function f(x). Suppose we have an approximation of the root xn which has an error of (r ...
Error Estimate for the Newton-Raphson Method
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To obtain the last line we expand the denominator using the binomial expansion and then neglect all terms that have a higher power of than the leading term. Thus, we …
Error bounds for the modified Newton's method - Cambridge ...
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Error bounds for the modified Newton's method - Volume 14 Issue 3. ... of the Kantorovich convergence theorem for the modified Newton's method is proved.
A unified derivation of several error bounds for Newton's process
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Finally, results on the Newton method in partially ordered space are surveyed. A method is also described for estimating the componentwise errors for ...
Sharp error bounds for Newton-like methods under weak ...
https://www.cambridge.org/core/journals/bulletin-of-the-australian...
Sharp error bounds for Newton-like methods under weak smoothness assumptions - Volume 45 Issue 3
Error bounds for Newton's iterates derived from the ...
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In this paper, it is shown that the upper and lower bounds of the errors in the Newton iterates recently obtained by Potra-Pták [11] and Miel [7], with the use of nondiscrete induction and majorizing sequence, respectively, follow immediately from the Kantorovich theorem and the Kantorovich recurrence relations. It is also shown that the upper and lower bounds of Miel are finer than those of ...
Optimal Error Bounds for the Newton–Kantorovich Theorem ...
epubs.siam.org › doi › 10
Jul 14, 2006 · Error Bounds for Newton’s Method Under the Kantorovich Assumptions. The Merging of Disciplines: New Directions in Pure, Applied, and Computational Mathematics, 197-208. (1986) Error bounds for Newton's iterates derived from the Kantorovich theorem.
Error bounds for Newton's Method | Physics Forums
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16.09.2012 · Hi, PF Sometimes it is not easy to find roots of functions. Newton gave a nice clue: the Newton's Method formula: ##x_{n+1}=x_n-\\dfrac{f(x_n}{f'(x_n)}##. My concern is, now that I have understood and practiced it, comprehend what I've sketched in the summary. This is all taken from "Calculus...
A method for finding sharp error bounds for Newton's method ...
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This paper gives a method for finding sharp a posteriori error bounds for Newton's method under the assumptions of Kantorovich's theorem. On the basis of this method, new error bounds are derived, and comparison is made among the known bounds of Dennis [2], Döring [4], Gragg-Tapia [5], Kantorovich [6, 7], Kornstaedt [9], Lancaster [10], Miel [11–13], Moret [14], Ostrowski [17, 18], Potra [19], and Potra-Pták [20].
Newton's method - error bounds - Mathematics Stack Exchange
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Let α be the true root. We can define the error en+1 in the estimate xn+1 in three different ways. Way 1: en+1=xn+1−α. If that is the definition, ...
Error bounds for Newton-like methods under Kantorovich ...
https://link.springer.com/article/10.1007/BF03167104
[1] J. E. Dennis, On the convergence of Newton-like methods. Numerical Methods for Nonlinear Algebraic Equations (ed. P. Rabinowitz), Gordon and Breach, New York, 1970, 163–181.
Error Bounds for Newton’s Method Under the Kantorovich ...
https://link.springer.com/chapter/10.1007/978-1-4612-4984-9_14
J. E. Dennis, Jr., “On the Kantorovich hypothesis for Newton’s method,” SIAM J. Numer.Anal., 6 (1969), 493–507. MathSciNet zbMATH CrossRef Google Scholar
Error bounds for Newton's iterates derived from the ...
https://link.springer.com/article/10.1007/BF01389444
In this paper, it is shown that the upper and lower bounds of the errors in the Newton iterates recently obtained by Potra-Pták [11] and Miel [7], with the use of nondiscrete induction and majorizing sequence, respectively, follow immediately from the Kantorovich theorem and the Kantorovich recurrence relations. It is also shown that the upper and lower bounds of Miel are …
A method for finding sharp error bounds for Newton's ...
https://link.springer.com/article/10.1007/BF01389624
1. Bartle, R.G.: Newton's method in Banach spaces. Proc. Amer. Math. Soc.6, 827–831 (1955) Google Scholar . 2. Dennis, J.E.: On the Kantorovich hypothesis for ...
Newton's method - error bounds - Mathematics Stack Exchange
math.stackexchange.com › questions › 180650
Show activity on this post. I just have a very brief question regarding the formula for error bounds in Newton's method. Depending on where you look, this will either be written as: e n + 1 ≈ f ′ ′ ( r) 2 f ′ ( r) e n 2. or: e n + 1 ≈ − f ′ ′ ( r) 2 f ′ ( r) e n 2.
Newton's method - error bounds - Mathematics Stack Exchange
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Error bounds for Newton-like methods under Kantorovich ...
https://link.springer.com/article/10.1007/BF03167811
Affiliations. Department of Secretarial Science, Matsuyama Shinonome Junior College, 790, Matsuyama, Japan. Toshio Konishi. Department of Mathematics, Faculty of ...
Error bounds for Newton's Method | Physics Forums
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Jan 18, 2022 · Hi, PF Sometimes it is not easy to find roots of functions. Newton gave a nice clue: the Newton's Method formula: ##x_{n+1}=x_n-\\dfrac{f(x_n}{f'(x_n)}##. My concern is, now that I have understood and practiced it, comprehend what I've sketched in the summary. This is all taken from "Calculus...