# Computational Science Stack Exchange Community Digest

## Top new questions this week:

### SINDy Vs standard methods for system identification

I have been trying to understand the recently proposed Sparse Identification of Nonlinear Dynamics SINDy. Despite several attempts, I seem to fail to understand the difference between SINDy and the ...

differential-equations least-squares machine-learning linear-system chaotic-systems asked by Chenna K Score of 3

### Correctness of direct numerical solution of ill-conditioned linear system

To what extent can you put trust in a numerical solution obtained by direct solver for an ill-conditioned linear system? In other words, how can you test the solution? Dropping it into the system says ...

numerics linear-solver linear-system condition-number asked by Fidel Pestrukhine Score of 3 answered by Federico Poloni Score of 7

Trying to solve numerically the 2D Poisson equation with variable diffusion coefficient $K$, that in general can be discontinuous. $$\frac{\partial}{\partial x} ( K(x,y)\frac{\partial C}{\partial x}) ... pde finite-difference poisson elliptic-pde asked by Millemila Score of 2 answered by Daniel Shapero Score of 4 ### How can I derive a second order implicit method for this coupled ODE update? I appreciate this might be an easy question, but I've managed to get myself quite thoroughly confused I'm trying to solve a system of physics equations that look as follows$$ \frac{\partial \mathbf{E}...

implicit-methods asked by mgmf46 Score of 1 answered by Lutz Lehmann Score of 1

### Min supporting line of a set of points

I am following along Rourke's book and I am trying to do the excercies mentioned in this SO post: Min supporting line for a set of points Design an algorithm to find a line 𝐿 that: has all the ...

optimization computational-geometry mesh geometry convex-hull asked by Makogan Score of 1

### How to scale gradients in a gradient descent algorithm?

I am training a neural network with the multiobjective steepest gradient descent algorithm. The want to steer the direction of the gradient descent so that I land up at a point slightly above where I ...

optimization scaling neural-network asked by Jeet Score of 1

### Finding the parameters of a function via curve fit

I'm trying to estimate the parameters (v, n, k) defined in fit_func. I tried the default least squares fit but I couldn't find the parameters successfully. ...

optimization python scipy approximation curve-fitting asked by Natasha Score of 1 answered by Lutz Lehmann Score of 5

## Greatest hits from previous weeks:

### Plot integral function with scipy and matplotlib

I want to plot a numerical integral function of some function $f$ using scipy and matplotlib. How can I do this? I tried the ... asked by student Score of 7 answered by GertVdE Score of 8

### How to code in Matlab: If an argument is empty, then default to "x" value?

I have a function with a number of arguments, but some of them are optional. 1.) If when the function is called, some are left empty, how do I code it so that it defaults to a specific value? 2.) ...

matlab asked by TheRealFakeNews Score of 7 answered by Nat Wilson Score of 7

### Is it possible for user written algorithms to outperform libraries' built-in optimized functions?

I've always had this question in mind (even if it may sound vague), but in my numerical analysis courses we've always learned how to analyze and optimize code. However, since most linear algebra ...

performance libraries asked by CynthiaZ1998 Score of 25 answered by Thijs Steel Score of 32

### Minimizing the Sum of Absolute Deviation (${L}_{1}$ Distance)

I have a data set $x_{1}, x_{2}, \ldots, x_{k}$ and want to find the parameter $m$ such that it minimizes the sum $$\sum_{i=1}^{k}\big|m-x_i\big|.$$ that is $$\min_{m}\sum_{i=1}^{k}\big|m-x_i\big|.$$...

optimization convex-optimization asked by mayenew Score of 16 answered by Dirk Score of 22

### What are some good strategies for improving the serial performance of my code?

I work in computational science, and as a result, I spend a non-trivial amount of my time trying to increase the scientific throughput of many codes, as well as understanding the efficiency of these ...

performance asked by Aron Ahmadia Score of 69 answered by Pedro Score of 69

### Complexity of matrix inversion in numpy

I am solving differential equations that require to invert dense square matrices. This matrix inversion consumes the most of my computation time, so I was wondering if I am using the fastest algorithm ...

numpy dense-matrix inverse asked by physicsGuy Score of 17

### Parallelizing a for-loop in Python

Are there any tools in Python that are like Matlab's parfor? I found this thread, but it's four years old. I thought maybe someone here might have more recent experience. Here's an example of the ...

python parallel-computing asked by Paul G. Constantine Score of 47 answered by Daniel Mahler Score of 24

## Can you answer this question?

### Crank-Nicolson vs Spectral Methods for the TDSE

The time-dependent Schroedinger equation (TDSE) depends linearly on the system's initial state $\vert \psi(0) \rangle$, such that the solution can be generally written as  \vert \psi(t) \rangle = \...

pde quantum-mechanics crank-nicolson operator-splitting asked by QuantumBrick Score of 1
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