#rootfinding — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #rootfinding, aggregated by home.social.
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Alright, future engineers!
**Newton-Raphson:** Iteratively finds function roots (where f(x)=0).
Formula: `x_n+1 = x_n - f(x_n) / f'(x_n)`
Pro-Tip: A poor initial guess can lead to divergence or finding the wrong root!
#NumericalMethods #RootFinding #STEM #StudyNotes -
Alright, future engineers!
**Bisection Method:** Finds f(x)=0 roots by repeatedly halving intervals where sign changes.
Ex: If `f(a)f(b)<0`, root's in `[a,b]`. `x_new = (a+b)/2`.
Pro-Tip: Guaranteed convergence if root is bracketed, but can be slow!
#NumericalMethods #RootFinding #STEM #StudyNotes -
Alright, future engineers!
**Newton-Raphson** finds roots of `f(x)=0` by iteratively refining guesses.
Ex: `x_new = x_old - f(x_old)/f'(x_old)`.
Pro-Tip: A good initial guess speeds up convergence & prevents divergence! -
Alright, future engineers!
**Newton-Raphson** is an iterative method to find function roots (where f(x)=0).
Formula: `x_n+1 = x_n - f(x_n)/f'(x_n)`
Pro-Tip: Your initial guess `x_0` matters! Pick one close to the root for faster convergence.
#NumericalMethods #RootFinding #STEM #StudyNotes -
Alright, future engineers!
The **Newton-Raphson Method** iteratively finds roots (where f(x)=0) using tangent lines.
Ex: `x_n+1 = x_n - f(x_n) / f'(x_n)`.
Pro-Tip: A good initial guess `x_0` is crucial for quick convergence!
#NumericalMethods #RootFinding #STEM #StudyNotes -
Alright, future engineers!
The **Bisection Method** finds roots by repeatedly halving an interval where `f(x)` changes sign. Ex: If `f(a)f(b) < 0`, a root is in `[a,b]`. Pro-Tip: Always converges, guaranteed if a root exists in the initial bracket!
#NumericalMethods #RootFinding #STEM #StudyNotes -
Alright, future engineers!
**Newton-Raphson:** Finds roots for f(x)=0 using tangent lines. Ex: `x_new = x_old - f(x_old)/f'(x_old)`. Pro-Tip: Needs `f'(x)`, but converges rapidly with a good initial guess!
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Alright, future engineers!
**Fixed-Point Iteration** finds a root by transforming `f(x)=0` into `x=g(x)` & iterating `x_new = g(x_old)`.
Ex: For `x^2 - x - 1 = 0`, try `x = sqrt(x+1)`.
Pro-Tip: Choosing the right `g(x)` is CRUCIAL for fast convergence! -
Alright, future engineers!
**Newton-Raphson** iteratively refines guesses to find function roots (zeros). Formula: `x_new = x_old - f(x_old)/f'(x_old)`. Pro-Tip: A *good* initial guess is crucial for quick, stable convergence!
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Alright, future engineers!
**Newton-Raphson:** Iteratively finds roots using tangent lines. Formula: `x_n+1 = x_n - f(x_n)/f'(x_n)`. Pro-Tip: A good initial guess is KEY to fast convergence!
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Alright, future engineers!
**Newton-Raphson** iteratively finds roots of f(x). Formula: `x_n+1 = x_n - f(x_n)/f'(x_n)`. Pro-Tip: A good initial guess is *key* for fast convergence!
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Newton-Raphson finds equation roots iteratively. Formula: x_n+1 = x_n - f(x_n)/f'(x_n). Pro-Tip: A good initial guess (x_0) is crucial for convergence! It can diverge if x_0 is poor.
#NumericalMethods #RootFinding #STEM #StudyNotes -
Newton-Raphson iteratively finds roots of f(x)=0 using tangent lines. Formula: `x_new = x_old - f(x_old) / f'(x_old)`. Pro-Tip: Your initial guess is critical; a bad one can lead to divergence!
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Newton-Raphson iterates to find equation roots by repeatedly approximating the tangent.
x_new = x_old - f(x_old)/f'(x_old)
Pro-Tip: Initial guess is crucial! A bad start can lead to divergence or wrong roots.