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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Newton-Kantorovich theorem: geometric intuition
I am trying to find some geometric intuition for the Newton-Kantorovich theorem, and I have investigated the special case of real numbers. The theorem states:
$$\textbf{The Newton-Kantorovich theorem}...
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Proof of Newton-Kantorovich theorem, Wikipedia version
Context
I have recently been researching the Newton-Kantorovich theorem after wondering about convergence criteria for the Newton-Raphson method in numerical analysis, as it seems to be the most ...
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How does extra equations affect Newton-Raphson method's performance on solving system of non-linear equations? [closed]
I'm working with model updating, in which the model's parameters are adjusted in order to reduce its ouput error in relation to a reference. For this, I would like to compare minimizing a single ...
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local superlinear convergence of Newton's method for C^1 functions
i am trying to prove, that there exists an $\epsilon>0$, s.t. for $f\in C^1([a,b])$ with $f(x_*)=0,\;f'(x_*)\neq0$ Newton's method converges superlinear for every starting point $x_0\in[x_*-\...
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Newton-Raphson Method's Convergence
I have a function with three real roots, for which I have to prove the following:
There are three intervals in which, for every initial guess, N-R converges to the root.
I have this Theorem from a ...
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How can I derive equation 2.23(Newton-Raphson for Entropy) in NASA CEA analysis
It might sound a bit basic, but, I'd like to follow NASA CEA report I. analysis from the beginning.
So, I have to derive the Newton-Raphson equation from the entropy equation, which is one of the ...
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Newton-Raphson algorithm proof: derivating a matrix
A particularly useful algorithm when you want to find the zero of a function is the Newton-Raphson method.
For simplicity, we begin by examining the simplest case. Given a function and his root $x^\...
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Problem with Newton's method (numerical analysis)
I am not understanding how to proceed with this exercise, which asks me to solve $f(x) = 0$ by using Newton's method. It asks me to study the convergence of the sequences $x_k$ (built with Newton's ...
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Newton raphson method in multidimension space
I have a question, and that is, lets say $e(w) = x - x* = w^T\phi - x^* \in \mathbb R^n$, where $w \in \mathbb R^{N\times n}$ and $\phi \in \mathbb R^N$ I wish to use Newton Raphson method to find the ...
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Scaling nonlinear system for iterative numerical solver
In Numerical Recipes (C++) there is a Globally convergent Newton Method that can be used to solve systems of nonlinear equations. For context this is section 9.7 (page 477) of the 3rd edition. ...
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Is there componentwise descent property of Newton's method
Consider Newton's method for minimizing $f:\mathbb{R}^2 \rightarrow \mathbb{R}$, which is the basically applying it for solving $\nabla f(X)=0$, where $X=(x,y)\in \mathbb{R}^2$.
The iteration of ...
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Choosing the initial seed point in Newton Raphson method
In Newton-Raphson method to find approximate roots I noticed 2 approaches being followed to choose initial seed points for a given equation f(x) and I am confused when to apply which method.
First ...
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Does the accuracy of the iterations of the Newton method transfer to parts of the underlying non-linear equation system?
I'm just wondering one thing. Suppose I have a non-linear system of equations $F(z) = z - d(z) = 0$ for $F: \mathbb{R}^{n} \longrightarrow \mathbb{R}^{n}$. If I apply a Newton method with respect to $...
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Tangent definition with a newton raphson question example
I'm very confused about the definition of a tangent, I was told its a straight line that touches a curve at a point, but if extended does not cross the curve at any other point.
In this question if u ...
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Newton root finding and preserving automatic differentiation.
I am applying Newton's root solving algorithm. Suppose the example problem below, solving for $g$ with fixed parameter, $s$:
$$ f(g;s) = g^2 - s = 0, \qquad g_{i+1}=g_i - \frac{f(g_i;s)}{\frac{df}{dg}(...
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