#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:** An iterative method to efficiently find the roots (where f(x)=0) of a function.
Ex: `x_n+1 = x_n - f(x_n)/f'(x_n)`
Pro-Tip: Your initial guess is CRUCIAL! A poor one can lead to divergence or the wrong root.
#NumericalMethods #RootFinding #STEM #StudyNotes -
**Bisection Method:** Finds `f(x)=0` roots by repeatedly halving an interval with a sign change.
Ex: If `f(a)f(b)<0`, a root is in `[a,b]`. New interval `c=(a+b)/2`.
Pro-Tip: Guaranteed to converge if `f(a)f(b)<0`, even if slow! No derivative needed.
#NumericalMethods #RootFinding #STEM #StudyNotes -
Alright, future engineers!
**Secant Method:** Finds `f(x)=0` roots via secant line using two prior points.
Ex: `x_n+1 = x_n - f(x_n) * (x_n - x_n-1) / (f(x_n) - f(x_n-1))`
Pro-Tip: No derivative needed! Faster than Bisection; requires two initial guesses.
#NumMethods #RootFinding #STEM #StudyNotes -
Alright, future engineers!
**Bisection Method:** Finds `f(x)=0` roots by halving intervals `[a,b]` where `f(a)` and `f(b)` have opposite signs.
Ex: `c = (a+b)/2`; update `[a,c]` or `[c,b]`.
Pro-Tip: Guaranteed to converge, but it's slower than others!
#NumMethods #RootFinding #STEM #StudyNotes -
Alright, future engineers!
**Newton-Raphson:** Iteratively finds roots of a function `f(x)=0`.
Ex: `x_n+1 = x_n - f(x_n)/f'(x_n)`
Pro-Tip: A good initial guess is KEY! Poor choices can lead to divergence or wrong roots.
#NumericalMethods #RootFinding #STEM #StudyNotes -
Alright, future engineers!
**Newton-Raphson:** Finds f(x)=0 roots by iteratively approximating them with tangent lines.
Ex: `x_n+1 = x_n - f(x_n)/f'(x_n)`
Pro-Tip: Super fast, but needs a good initial guess and the derivative f'(x)!
#NumMethods #RootFinding #STEM #StudyNotes -
Alright, engineers!
**Bisection Method:** Finds f(x)=0 roots by repeatedly halving an interval where f(x) changes sign.
Ex: If f(a)<0 & f(b)>0, root is in [a,b]. Midpoint splits it.
Pro-Tip: Guarantees convergence if you bracket a root!
#NumMethods #RootFinding #STEM #StudyNotes -
Alright, future engineers!
**Newton-Raphson:** Iteratively finds function roots (where f(x)=0) by using tangent lines to approximate the next guess.
Ex: `x_new = x_old - f(x_old) / f'(x_old)`
Pro-Tip: A good initial guess is KEY for quick convergence!
#NumericalMethods #RootFinding #STEM #StudyNotes -
Alright, future engineers!
**Bisection Method:** Systematically finds a root by repeatedly halving an interval where a sign change indicates a root's presence.
Ex: If `f(a)<0` & `f(b)>0`, root is in `[a,b]`. New interval is `[a, (a+b)/2]` or `[(a+b)/2, b]`.
Pro-Tip: It ALWAYS converges (given a sign change!), but it's often slower than other methods.
#NumMethods #RootFinding #STEM #StudyNotes -
Alright, future engineers!
**Newton-Raphson:** Iteratively finds roots of f(x)=0 by approximating with tangent lines.
Ex: `x_n+1 = x_n - f(x_n)/f'(x_n)`
Pro-Tip: A good initial guess is crucial for fast convergence and to avoid divergence!
#NumMethods #RootFinding #STEM #StudyNotes -
**Bisection Method:** Finds `f(x)=0` roots by repeatedly halving an interval with a sign change.
Ex: If `f(a)f(b) < 0`, root in `[a,b]`. New `c=(a+b)/2`.
Pro-Tip: Slow but *guaranteed* convergence if a root is bracketed. Reliability first!
#NumMethods #RootFinding #STEM #StudyNotes -
Alright, future engineers!
**Newton-Raphson:** Iteratively finds roots of f(x)=0 by following tangent lines to approximate the zero.
Ex: `x_n+1 = x_n - f(x_n)/f'(x_n)`
Pro-Tip: A good initial guess means faster, surer convergence!
#NumMethods #RootFinding #STEM #StudyNotes -
Alright, future engineers!
**Newton-Raphson:** Iteratively finds function roots by following tangent lines to the x-axis.
Ex: `x_next = x_curr - f(x_curr) / f'(x_curr)`
Pro-Tip: Requires a good initial guess! A near-zero `f'(x)` can cause divergence.
#NumMethods #RootFinding #STEM #StudyNotes -
Alright, future engineers!
**Newton-Raphson:** Iteratively finds roots of `f(x)=0` by repeatedly refining an estimate.
Ex: `x_n+1 = x_n - f(x_n)/f'(x_n)`
Pro-Tip: A good initial guess (close to the actual root) vastly improves convergence speed!
#NumericalMethods #RootFinding #STEM #StudyNotes -
Alright, future engineers!
**Bisection Method:** Finds roots of `f(x)=0` by repeatedly halving an interval where `f(x)` changes sign.
Ex: If `f(a)f(b)<0`, a root lies between `a` and `b`.
Pro-Tip: Guaranteed to converge (slowly!) if a root exists in your initial bracket – very robust!
#NumericalMethods #RootFinding #STEM #StudyNotes -
Alright, future engineers!
**Newton-Raphson:** Iteratively finds roots of f(x)=0 by following tangent lines to the x-axis.
Ex: `x_new = x_old - f(x_old)/f'(x_old)`
Pro-Tip: Super fast convergence, but needs a good initial guess and `f'(x)` not zero!
#NumericalMethods #RootFinding #STEM #StudyNotes -
Alright, future engineers!
**Newton-Raphson Method:** Iteratively finds a function's root (where f(x)=0).
Formula: `x_n+1 = x_n - f(x_n)/f'(x_n)`
Pro-Tip: A good initial guess is crucial for rapid convergence!
#RootFinding #NumericalMethods #STEM #StudyNotes -
Alright, future engineers!
**Newton-Raphson:** An iterative method to find roots (zeros) of a function.
Formula: `x_new = x_old - f(x_old) / f'(x_old)`
Pro-Tip: A good initial guess is CRUCIAL for fast convergence! -
Alright, future engineers!
**Newton-Raphson:** An iterative method to find roots (zeros) of a function.
Formula: `x_new = x_old - f(x_old) / f'(x_old)`
Pro-Tip: A good initial guess is CRUCIAL for fast convergence! -
Alright, future engineers!
**Newton-Raphson:** Iteratively finds roots `f(x)=0` by following tangent lines.
Ex: `x_new = x_old - f(x_old) / f'(x_old)`
Pro-Tip: A good initial guess is CRUCIAL for fast convergence (or any convergence)!
#NumericalMethods #RootFinding #STEM #StudyNotes -
Alright, future engineers!
**Newton-Raphson:** Iteratively finds roots `f(x)=0` by following tangent lines.
Ex: `x_new = x_old - f(x_old) / f'(x_old)`
Pro-Tip: A good initial guess is CRUCIAL for fast convergence (or any convergence)!
#NumericalMethods #RootFinding #STEM #StudyNotes -
Alright, future engineers!
**Bisection Method:** Finds roots by repeatedly halving an interval where a sign change occurs.
Ex: If f(a)*f(b) < 0, root is in [a,b]. New midpoint c=(a+b)/2.
Pro-Tip: Slow but *guaranteed* to converge if a root is bracketed!
#RootFinding #NumericalMethods #STEM #StudyNotes -
Alright, future engineers!
**Bisection Method:** Finds roots by repeatedly halving an interval where a sign change occurs.
Ex: If f(a)*f(b) < 0, root is in [a,b]. New midpoint c=(a+b)/2.
Pro-Tip: Slow but *guaranteed* to converge if a root is bracketed!
#RootFinding #NumericalMethods #STEM #StudyNotes -
Alright, future engineers!
**Newton-Raphson** iteratively finds roots of `f(x)=0` by using tangent lines.
Formula: `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!
**Newton-Raphson** iteratively finds roots of `f(x)=0` by using tangent lines.
Formula: `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!
**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!
**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!
**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** 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!
**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 **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!
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!
**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!
**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 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!
-
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!
-
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. -
`We show that the Weierstrass method, like the well known #Newton method, is not generally convergent: there are open sets of #polynomials p of every degree d≥3 such that the dynamics of the Weierstrass method applied to p exhibits attracting periodic orbits.`
https://arxiv.org/abs/2004.04777
#rootFinding #optimizationTheory #optimization #computation #computing