#numericalmethods — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #numericalmethods, aggregated by home.social.
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PhD Position on Numerical Simulation of Biological Interfaces
TU FreibergSee the full job description on jobRxiv: https://jobrxiv.org/job/tu-freiberg-27778-phd-position-on-numerical-simulation-of-biological-interfaces/
#biomathematics #biophysics #numericalmethods #simulation #ScienceJobs #hiring #research
https://jobrxiv.org/job/tu-freiberg-27778-phd-position-on-numerical-simulation-of-biological-interfaces/?fsp_sid=11801 -
Alright, future engineers!
**Euler's Method:** Approximates solutions to differential equations by taking small linear steps.
Formula: `y_n+1 = y_n + h * f(x_n, y_n)`
Pro-Tip: Smaller step size (h) improves accuracy but increases computational cost! -
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 -
**Truncation Error:** Inaccuracy from approximating infinite math processes (e.g., series) with finite steps.
Ex: Using `x` for `sin(x)` near 0.
Pro-Tip: It's an error in the *method*, not computer precision.
#NumericalMethods #Error #STEM #StudyNotes -
Approximating Hyperbolic Tangent
https://jtomschroeder.com/blog/approximating-tanh/
#HackerNews #ApproximatingTanh #HyperbolicFunctions #MathBlog #ComputationalMath #NumericalMethods
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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!
**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!
**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** 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** 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!
**Truncation Error** occurs when an exact mathematical procedure is replaced by an approximation, often by cutting off an infinite series.
Ex: Using only the first few terms of a Taylor series for `e^x`.
Pro-Tip: This error is *predictable* and *controllable* by refining your approximation!
#NumericalMethods #ErrorAnalysis #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!
**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!
**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!
**Trapezoidal Rule:** Approximates `∫f(x)dx` by summing areas of trapezoids under the curve.
Ex: For one segment, `∫f(x)dx ≈ (b-a)/2 * (f(a) + f(b))`.
Pro-Tip: Use more segments (smaller `h`) for better accuracy!
#NumericalMethods #Integration #STEM #StudyNotes -
Alright, future engineers!
**Relative Error:** Quantifies how much an approximation deviates, *relative to the true value*. Ex: `RE = |(Approx - True) / True|`. Pro-Tip: Essential for evaluating precision and setting engineering tolerances!
#NumericalMethods #ErrorAnalysis #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 **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 **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!
**Euler's Method:** Approximates solutions to ODEs by taking small linear steps. Ex: `y_new = y_old + h * f(x_old, y_old)`. Pro-Tip: Accuracy depends heavily on step size `h`. Smaller `h` is better for precision!
#ODEs #NumericalMethods #STEM #StudyNotes -
Alright, future engineers!
**Truncation Error** is the inaccuracy from ending an infinite math process (like a series or integral) at a finite step. Ex: `e^x` approximated by `1+x`. Pro-Tip: You can *control* it by adjusting step size or terms, unlike round-off error!
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PhD Position on Numerical Simulation of Biological Interfaces
TU FreibergSee the full job description on jobRxiv: https://jobrxiv.org/job/tu-freiberg-27778-phd-position-on-numerical-simulation-of-biological-interfaces/
#biomathematics #biophysics #numericalmethods #simulation #ScienceJobs #hiring #research
https://jobrxiv.org/job/tu-freiberg-27778-phd-position-on-numerical-simulation-of-biological-interfaces/?fsp_sid=11177 -
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!
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!
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!
**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!
-
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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Released my DIA-format Gauss-Seidel smoother plugin for OpenFOAM v13. MIT licensed.
Replaces the default LDU smoother on structured hex meshes — DIA stores diagonal bands contiguously, reducing pointer indirection and DRAM pressure. Expecting 10–20% wall-clock gains and better cache utilisation based on standalone profiling. Full OpenFOAM benchmarks incoming.
https://github.com/amartyadav/DIAGaussSeidel-Smoother-OpenFOAM
#OpenFOAM #HPC #CFD #NumericalMethods #FOSS #computerscience #physics
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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!
**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!
**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!