# 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.

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### Existence of bounded derivative inverse (Deuflhard Exercise 1.1)

The following exercise is from Deuflhard's "Newton Methods for Nonlinear Problems" : Given a nonlinear $C^1$-mapping $F:X\to Y$ over some domain $D\subset X$ for Banach spaces $X$, $Y$, each endowed ...
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### Is it possible to use Newton's method on a function with an integral?

So I have a root solving problem where I want to find x, but my equation is: $$0=1-p+c_2\int_0^Xt^{\alpha-1}e^{-t/2}dt$$ where $0\le p\le1, c_2\ge2$, $1\le\alpha$. Is it possible to use Newton's ...
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### newton raphson question [closed]

Find a cut point of the $y = x^3-4x-5$ and $y = e^x-4x-5$ curves by selecting the starting point $x_0 = 3$, using the Newton Raphson method with an error of $10^{-3}$ I can't solve the question. Can ...
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### Convergence of Halley's method at a Root $x = p$ of $f(x)$

Define an iterative method for finding the roots of a function $f(x)$ by $$p_{n+1} = p_n − \frac{f(p_n)f'(p_n)}{f'(p_n)^2 - \frac{1}{2}f(p_n)f''(p_n)}$$ where $f(x)$ is at least twice differentiable....
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### Selecting guess matrix for Newton method to calculate inverse of a matrix

I have implemented the newton method as follows to calculate inverse of a matrix(input in my case)and x0 being the initial guess matrix.But the value of the iteration is not stable.I suspect the ...
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### Newton Method (Root Finding) Theoretical Problem convergence of $x_{n+1} = x_n - \lambda f(x_n)$

$f(x)$ is a function such that for every $x$, $f'(x)$ is well defined and $0<m<f'(x)<M$. We are using a Newton-like method to find its root. consider sequence $x_{n+1} = x_n - \lambda f(x_n)$ ...
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### Finding all positive real roots of $e^x - x -2 = 0$ using Newton Raphson's method.

How should I go approach this problem if I need to solve this problem by hand? Is there a general formula that I can use?
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### Multivariate Newton-Raphson in R language (equations that contains integral)

I am trying to apply multivariate Newton-Raphson method using R language. However I have encountered some difficulties to define functions which includes the integral in the equations. For instance, ...
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### Problem about applying the Newton's method to a system

Problem The amount of pressure needed to sink an object in a bed of homogeneous soft soil that lies above a base of hard soil can be estimated using the pressure needed to sink smaller objects into ...
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### Minimum iterations to guarantee a forward error of $\epsilon$

can anyone shed some light into this for me. I am asked to numerically solve $$x\arctan(x) = 1$$ and to ensure that the error $\epsilon$ is less than $10^{-3}$. Now I usually use Newton's method for ...
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### Darboux' theorem on the convergence of Newton's method

I've only found the text in French, which I just don't read well enough to understand what is going on. Any pointers to a clear proof in English? The paper is Darboux, "Sur la méthode d'approximation ...
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I have an analytical function $f:\mathbb{R}^n\to\mathbb{R}$ that I want to minimise using Newton's method. Given a point $\mathbf{x}_i\!\in\!\mathbb{R}^n$, I compute the gradient, $\nabla\! f(\mathbf{... 2answers 21 views ### How to find$x_1$? let$f(x) =x^2-5$for$x \in \mathbb{R}$. Let$x_0 =1$. If$\{x_n\}$denotes the sequence of iterates defined by the newton -raphson method to approximate a solution of$f(x)=0$. Find$...
If I have a multivariate function f twice differentiable which is strongly convex, and smooth as well, so $\mathit \nabla ^2f - \mu I$ and $\mathit LI - \nabla ^2 f$ are both positive definite at ...
I have a function $f:\mathbb{R}^n\to\mathbb{R}$ with an analytical expression. The function itself is very complicated, so I will omit the definition for brevity. It is a highly non-linear function ...