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Questions tagged [newton-raphson]

This tag is for questions regarding the Newton–Raphson method. In numerical analysis the Newton–Raphson method is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.

The Newton–Raphson method in one variable is implemented as follows:

The method starts with a function $f$ defined over the real numbers, the function's derivative $f'$, and an initial guess $x_0$ for a root of the function $f$. If the function satisfies the assumptions made in the derivation of the formula and the initial guess is close, then a better approximation $x_1$ is $$x_1 = x_0 -\frac{f(x_0)}{f'(x_0)}$$

The process is repeated as

$$x_{n+1} = x_n -\frac{f(x_n)}{f'_n(x_n)}$$

until a sufficiently accurate value is reached.

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Computational complexity of $1/(x+z)$.

Is there a fast method to calculate $1/(x+z)$ where $z$ is a root of unity and $x$ is real. By fast computation, I mean is there a faster method than Newton-Rhaphson method.
Bhavesh Lakhotia
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Newton's Method on $f(x)=\arctan(x)$ with oscillation

Consider the function $f(x)=\arctan(x)$ defined on $\mathbb{R}$. Let $x_0\neq0$ be an initial guess for the root of $f$ and apply Newton's Method with $x_0$. Further assume that the iterations produce an oscillating sequence…
Silver Pine
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Find correct to 6 decimal places, the x-coordinate of the point on the curve y = ln x which is closest to the origin.

I must use the Newton Raphson method. Can someone please explain the steps I must take in order to reach the answer. For alot of this im having to self study the material to catch up and without instruction, im quite lost on how to approach the…
margiela
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Is Newton-Raphson the best we can do if we only know the derivative?

I was wondering if NR is the fastest method to find a root if all we know about a function is how to evaluate it and its derivative at any point. Since you can use the first derivative to approximate the second I was wondering if this lets you…
Salamander
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Newton method exchanging row

suppose to have a function $F(x,y,z) = [ f_1(x,y,z),f_2(x,y,z),f_3(x,y,z)]$ and that $f_1$ depend only by x, $f_2$ depends only by y and $f_3$ depends only by z. Now if I apply newton method I can write $[d_x,d_y,d_z] =…
Carl
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Newton method and machine learning

There is some debate about why Newton method is not widely used in machine learning. Instead, people tend to use gradient descent. Some people claim that Newton method is not used because it involves the second derivative. How so? Indirectly? …
Daniel S.
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Finding the orthogonal projection onto a surface

I have a smooth $n-1$-surface embedded in $R^n$. I have a way to find a point on the surface along a given line, and a way to compute the tangent plane at a given point on the surface. I would like to find the orthogonal projection of an arbitrary…
Him
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How to find the cube root of 10 using Newton Raphson Method

How to find the cube root of $10$ by Newton-Raphson method correct up to $5$ significant figures?
Tilak Bhattacharya
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how to detect the points on which Newton Raphon method will give a oscillating sequence.

Example consider the function $x^3 -x/2 +1/4$.. we have a oscillation if we start from 0 or 0.5 in Newton Raphson Sequence. Why this oscillation pattern observed and how to detect it?
Nivedit Jain
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Newton-Raphson method issue

I have a quick question. I have a system of residuals in the form of $$R_i= (\sum_{j=1}^n a_{ij}x_j)-b_i$$ where $a_{ij}$ and $b_{i}$ are constants. I am trying to show that applying Newton-Raphson to this system of equations will converge to a…
Patrick
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Newton-Raphson convergence issue

I am working with the following function where r= 2^(-d) and d =[1:100] I am comparing 5 different algorithms to compute the roots of this function but the Newton Raphson method doesn't converge anymore above a certain value of r. Column n°5 on…
Yrden
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estimation of error - Newton-Raphson method

I am trying to write code that solves equations using Newton-Raphson method. I want the iterations would stop when the error is smaller than the tolerance defiend by the user. How can I validate the error is smaller than the tolerance? thanks
user213158
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Newton Raphson method to find intersection points

I'm supposed to use N-R method to find intersection point near $(4,-4)$ of $x^2+y^2=16$ and $e^{1/3x} + (1/5)y =1 .$ So, I equated these two functions, and got $f(x) = 5- (5*\exp(x/3)) + (16- x^2)^{1/2}$ and $f'(x)= (-5/3)*\exp(x/3) -…
carsof
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double roots with Newton-raphson method

While working on an engineering problem, we have met a non linear system of two variables and two equations. $$ \left\{ \begin{array}{c} A=x \sin y \\ B=-x^2 + x \cos y \end{array} \right. $$ where $A$ and $B$ are constants. if the system is…
Lahouaria
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Why does the Newton-Raphson method always work?

Why does the Newton-Raphson method for solving equations always work? What I know: I know that if $f(x) = 0$, then the Newton-Raphson method may be applied. It states that $$x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$$ where the solution to $f(x) = 0$ is…
Xetrov
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