invariant - newton-raphsonEssays on algorithms and data structures by Ali Khalilli. Binary search, numerical methods, dynamic programming, graphs, strings.Zola2021-12-21T00:00:00+00:00https://invariant.khalilli.ai/tags/newton-raphson/atom.xmlNewton–Raphson2021-12-21T00:00:00+00:002021-12-21T00:00:00+00:00
alikhalilli
https://invariant.khalilli.ai/blog/newton-raphson/<p>Using the square-root finding technique as an example, this chapter will examine the Newton-Raphson approach in further detail. The in-depth examination and distinctions between <strong>Gradient Descent</strong> and <strong>Newton-Raphson</strong> will be the subject of a future season.
The Newton-Raphson technique is another numerical method for determining the square root. The root of a nonlinear equation must be bracketed by two estimations using methods like the bisection technique and the false position method. Bracketing approaches are used to accomplish this. Because they reduce the interval between the two estimations in order to zero in on the equation’s root, these approaches are always convergent.</p>
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<div class="pl-4"><p>The root is not bracketed in the Newton-Raphson approach. When it comes to solving an equation, just one initial guess of the root is required to get the iterative process started.
As a result, it might be considered an open approach. Open approaches may or may not converge, but if they do, it will be substantially faster than with bracketing.</p>
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<table><thead><tr><th></th><th>Bracketing (bisection, false position)</th><th>Newton-Raphson (open)</th></tr></thead><tbody>
<tr><td>Initial guesses</td><td>two estimations</td><td>one initial guess</td></tr>
<tr><td>Convergence</td><td>always convergent</td><td>may or may not converge</td></tr>
<tr><td>Speed</td><td>slower</td><td>substantially faster</td></tr>
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