New answers tagged algorithms
4
Yes. You can run rank-revealing QR on your matrix $A$, which will stop at step $k$ (hence effectively terminating in $O(mnk)$) and produce $A = QRP$, where $R$ has nonzeros only in its first $k$ rows, and $Q,P$ are orthogonal. You can now compute and SVD of $R$, and use it to piece back the factors with a few matrix products with cost $O(\max(m,n)k^2)$.
2
Another solution is to solve with solve_ivp and use the dense_output option which allows interpolating between solution steps:
import numpy as np
from scipy.integrate import ode, solve_ivp
import matplotlib.pyplot as plt
import warnings
def f(t,y):
l = 1
m = 1
d = 1
g = 9.8
return [y[1], -np.sin(y[0])*g/l-y[1]*d/m]
y0, t0 = [np.pi/2, 0], 0
...
4
Many numerical tips and theoretical explanations can be found in this book from Hairer and Wanner:
https://www.springer.com/gp/book/9783540566700
In this book, a strategy is described, which uses a time step such that the relative variation of the solution during the first time step is below a certain threshold if you were using explicit Euler (omitting the ...
4
I just found out about Voronoi particle tracking so i'm definitively not an expert. I just want to share what I have found to help others on there journey.
The author of the posted Shadertoy examples has a blog where he talks about it: https://michaelmoroz.github.io/Reintegration-Tracking/
Some papers that are talking about it are not behind a paywall (...
Top 50 recent answers are included
