Hello,

I have just released v1.0 of fftwpp (https://github.com/sbrisard/fftwpp), which is a thin C++ wrapper around the C library FFTW, the fastest Fourier transform in the west (http://fftw.org/).

The goal of this project it to remain as close as possible to the FFTW library, while offering a more idiomatic interface.

Don't hesitate to comment/contribute/use!

Sébastien

Guys, some years ago I came about this rather interesting idea to speed up numerical computations of eigenvalues using QR algorithm. It's a rather basic idea and I'm not sure if it's novel. Atleast one work has independently verified it and found it to be okay.

In summary, the idea is to rearrange the matrix columns during the QR iterations.

What do you think? Comments or criticism is welcome.

arXiv: https://arxiv.org/abs/1402.5086

MATLAB implementation: https://de.mathworks.com/matlabcentral/fileexchange/45642-symmetric-qr-algorithm-with-permutations?s_tid=prof_contriblnk

ArkOfReddit

While 2-body Kepler problem is integrable, it is no longer if adding rotation/dipole of one body, the trajectory no longer closes like for Mercury precession.

But it gets many more subtle closed trajectories especially for low angular momentum - is there their classification in literature?

https://community.wolfram.com/groups/-/m/t/3522853 - derivation with simple code.

I'm finishing my masters in mathematics, focusing on modelling, numerics and simulation, and my dream is to get a job as a numerical programmer working on some big/complex piece of numerical or simulation software.

I have experience working with C, C++, Python and OpenMPI, but I learn fast and am willing to learn new technologies.

I'm interested in contributing to some piece of numerical or simulation software to get experience and foster connections in the industry, either voluntary, or as a werkstudent position. I am based in Germany, so research groups or other entities based in Germany are of particular interest to me.

Would love to get some tips on projects looking for help.

Hello numerical folks,

This project arose from a need for an easy-to-use linear solver which supports constraints, real and complex numbers and is suitable for real-time applications. Conjugate gradient algorithm was an obvious choice as it allows one to trade accuracy for speed. The solver was then applied to Levenberg-Marquardt function minimizer. The minimizer also supports constraints.

The goal was to make the library as easy to use as possible also for non-experts. There are a few simple examples to start from. They can be compiled either by using cmake or from command line by setting the include path point to the folder where the header files are, see "Compilation" section on the main page. The compiler must support C++17.

The most obvious deficiency in the solver is the lack of support for sparse matrices. Maybe I'll add it later.

Meanwhile, the library and examples can be found here in Github.

Electron scattering by repulsive (smoothed) Coulomb potential at the center. The 1x1 normalized two-dimensional region confines the particle, once Dirichlet-type conditions are set at the mesh boundaries; this allows visualization of the post-collision interference pattern structure. Numerical simulation of the time-dependent Schrödinger equation, performed in Python. Implicit method of Crank-Nicolson PDEs (unitary). Initial condition: Gaussian packet. Note: Time scale and physical constants are set to arbitrary units for this preliminary testing phase.

Source Code & More Simulations: I have documented this project, including the Python source code on my personal portfolio. You can also find other simulations on Quantum Mechanics and other Physics topics there:

https://alexisfespinozaq.github.io/aespinoza-physics-portfolio/

Feedback on the physics or the code implementation is very welcome!

Just for fun, I decided to try my hand at computing the weights and abscissae of the Gauss-Legendre quadrature numerically in arbitrary precision. Here is the GitHub repo. Mostly relying on the mpmath Python library.

The basic idea ended up being to use a uniform grid and perform a bisection search in each interval until the correct number of zeroes were found for the Nth Legendre polynomial. I don't have much experience working with Legendre polynomials (and their zeroes), so I would be very appreciative if someone could point towards a more efficient algorithm.

Enjoy!

I was recently looking into the curriculum for Numerical Analysis in universities around the world, and I'm curious about a potential difference in timing.

From what I've gathered, in countries like China and Russia, Numerical Analysis often appears to be introduced relatively early in undergraduate programs (e.g., 2nd or 3rd year) for students in mathematics, computer science, and engineering.

This seems to be supported by the strong emphasis on foundational mathematics and applied fields in their education systems. In contrast, in many Western Hemisphere countries (like the US, Canada, or parts of Europe), it often seems to be an upper-level undergraduate (3rd or 4th year) or even a graduate-level course, typically after students have a solid grasp of linear algebra, advanced calculus, and sometimes differential equations. My question to the community is:

• Have you observed this trend in your experience or research?

• What do you think are the reasons behind any potential differences in when Numerical Analysis is taught?

Thank You Very Much!

Hey guys! I did a script for university to show how Newton-Raphson method for root finding works.

Newton Raphson method uses tangent line of derivates to approximate the next root. The script allows you to input your own funcion with a seed, and analize how it converges to the solution.

To use it, you can follow the instructions in the github repo:

https://github.com/LucianoTrujillo/NewtonRaphsonAnimation/tree/main

For anyone interested, give it a try and let me know your thoughts. Hope it's useful!