#OTD fifty years ago, death on a return visit to his native Hungary of the Mathematician, Theoretical Physicist and Numerical Analyst Cornelius Lanczos. Emeritus Professor in @DIAS_Dublin. #NumericalMethods #MathematicsHistory #LinearAlgebra

“How Does A Computer/Calculator Compute Logarithms?”, Zach Artrand (https://zachartrand.github.io/SoME-3-Living/).

Via HN: https://news.ycombinator.com/item?id=40749670 (which provides important addenda)

Nice:

“Taming Floating Point Sums”, Orson Peters (https://orlp.net/blog/taming-float-sums/).

Via HN: https://news.ycombinator.com/item?id=40477604

On Lobsters: https://lobste.rs/s/lps7qx/taming_floating_point_sums

El año empieza con publicaciones a todo lo que da. Apenas sacamos otro libro, de Métodos Numéricos y Matlab, en el que tuve el gusto de participar con un par de colegas. ¡A la venta en México acá! #book #science #MATLAB #numericalmethods
https://www.amazon.com.mx/dp/B0CZPJRXQH

"Floats Are Weird", Anthony Wang (https://a.exozy.me/posts/floats-weird/).

Via HN: https://news.ycombinator.com/item?id=39426341

On Lobsters: https://lobste.rs/s/2axq6g/floats_are_weird

See also: "The Right Way To Calculate Stuff" [2003], Don Hatch (http://www.plunk.org/~hatch/rightway.html).

Whenever I walk to/from home, I have to walk up/down an inclined street; I noticed that the asphalt floor has different curvatures depending on how near it is of a bend, and I try to find a less steep incline while walking.

This got me inspiration for the few questions below. Any simple explanations, and related links, are welcome.

Given a #differentiable surface within R^3, and two distinct points in it, there are infinitely many differentiable paths from one point to another, remaining on the surface. At each point of the #path, one can find the path's local #curvature. Then:

- Find a path that minimizes the supreme of the curvature. In other words, find the "flattest" path.

- Find a path that minimizes the variation of the curvature. In other words, find a path that "most resembles" a circle arc.

Are these tasks always possible within the given conditions? Are any stronger conditions needed? Are there cases with an #analytic solution, or are they possible only with numerical approximations?

I have just discovered that I have been pronouncing Runge-Kutta wrong for the last 25 years. Plus Carl and Wilhelm were both German.

#NumericalModelling #NumericalMethods
#DummKopf

I made a short blog post on using Newton's and Halley's method (with #Python code!). Newton's method is well known, Halley's less so but it converges even faster. https://www.moseleyinstruments.com/blog/newton_and_halley/ #programming #numericalmethods

Interesting ...

Combining Physics-Informed Neural Networks (PINNs) w. Classical Numerical Methods
https://old.reddit.com/r/MachineLearning/comments/15u8wky/r_combining_physicsinformed_neural_networks_pinns

* 2 papers try to reconcile/harmonize classical methods (finite difference) w. PINN

https://northboot.xyz/search?q=Neural+operators

Neural Operator: https://zongyi-li.github.io/neural-operator
Neural Operator: Learning Maps Between Function Spaces: https://arxiv.org/abs/2108.08481
Physics-Informed Deep Neural Operator Networks: https://arxiv.org/abs/2207.05748

Last activities in my course of #NumericalMethods, the #MonteCarlo method applied to: (1) the 2D #IsingModel on a lattice with different boundary conditions, and (2) the #PottsModel for $q=3$ in a 2D lattice with periodic boundary conditions.

My #fortran codes are still the fastest!

I added #ATS to the #RosettaCode for Adaptive Simpson Quadrature: https://rosettacode.org/wiki/Numerical_integration/Adaptive_Simpson's_method#ATS

I also made some revisions to the text of the draft task.

Exciting times in my course of #numericalmethods: we are studying Monte Carlo methods applied to the #IsingModel

#NumericalMethods student problems:

TFW you're scrambling to get enough done before deadline and it hits you that a nontrivial swath of your troubleshooting headaches is you didn't put as many decimal places in your answer as the order of magnitude of the error bound bc the problem on error bound came *after*

ISTG I'm going to put calculating error bounds with "nice" assumptions right there in the function

Any special function specialists around here? Are there good numerical methods to evaluate bivariate (hyper2d) hypergeometric functions/Kampé de Fériet functions besides evaluating the inner hypergeometric function and summing up? #numerics #numericalmethods #specialfunctions

Mastodon #introduction: TuxRiders is a journey to research experiences using free and #opensource scientific computing programs, which aimed to demonstrate their power for real-world scientific research.

In our #YouTube channel, we regularly talk about #FiniteElement, #EngineeringMath, #PDEs, #NumericalMethods, #FreeFEM, #FEniCS, #ParaView, #C++, #Python, #OpenFOAM, and #Linux.

Check out our YT channel: https://www.youtube.com/TuxRiders

Hello all. Going to give Mastodon a try. Here's my #introduction:

I'm a #ComputerGraphics professor at Dartmouth College. I do research primarily in physically based #rendering, particularly #MonteCarlo and volumetric/participating media rendering, and also a bit in digital #fabrication.

I also teach courses in #ComputerGraphics, #Rendering, #ComputationalPhotography, #LinearAlgebra, #NumericalMethods.
You can find my projects on my github page, including HDRView, SamplinSafari, rendering-bib.

Sorry for decreasing the signal/noise ratio, but I just realized the obligatory tag cloud is obligatory.
#science #mechanics #fluidmechanics #simulation #numerical #numericalmethods #data #datavisualization #multiphase #twophase #flow #maths #mathematics #physics #engineering #CORIA #Sorbonne #turbulence #fragmentation #emulsions #levelset #VOF #volumeoffluid #largeeddysimulation #fsi #fluidstructure #droplets #bubbles #surface #surfacetension #geometry #topology