# All Questions

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### Numerically solving a non-linear PDE

I have this non-linear partial differential equation. $$\frac{\partial C}{\partial t}=\left(\frac{\partial C}{\partial x}\right)^2+C\frac{\partial^2 C}{\partial x^2}$$ I want to use the finite ...
73 views

### Double mach reflection at a inclined wedge

I am running into a strange problem when solving the 2D compressible Euler equations on a inclined wedge. To elaborate, my top boundary condition seems to emitting some type of instability. I have ...
45 views

### Augmented Lagrangian Techniques Frank-Wolfe Algorithm [python]

I'm trying to solve the convex quadratic problem (quadratic min cost flow problem) using the Frank-Wolfe algorithm. $$\min\{x^TQx+qx: Ex=b,\quad 0\leq x \leq u\}$$ The standard algorithm is okay ...
41 views

### Singular Spectrum Analysis Explanation

I need you to help me understand the Singular Spectrum Analysis algorithm. I already read a lot of articles about the subject but they never answered my questions like what is the mathematical reason ...
75 views

### How to compute the determinant of Hessian of a multivariable function?

I have a function $F(\vec x)$ of many variables (let's say in the order of hundreds of thousands). I need to compute the determinant of the Hessian matrix at the point $x_0$. Is there a way to ...
53 views

### Bound for Expectation of Singular Value

In my case, $X_{\boldsymbol{\delta}}\in\mathbb{R}^{d\times M}$ is a function of Rademacher variables $\boldsymbol{\delta}\in\{1,-1\}^M$ with $\delta_i$ independent uniform random variables taking ...
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### How to integrate the contents of a vector using an adaptive quadrature routine [duplicate]

I have a function which requires the return type to be a container. The problem is that I need to integrate the contents of the container as efficiently as possible and was hoping to use adaptive ...
118 views

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### Specifying mesh spacing for DFT in numpy

I was testing the .fft package of numpy 1.16.1 in Python 3.7.2. In particular I was trying to verify that the transform resembles the analytical one for: f(x) = \mathrm{exp}\left[-\left(\frac{x-5}{2}...
63 views

### FFT solver for the Poisson problem with Dirichlet boundary conditions

I am trying to solve the Poisson problem with Dirichlet boundary condition in 1D: \begin{array}{rcl} - \mu \Delta u & = & f~in~[0,1], \\ u(0) & = & 0, \\ u(1) & = ...
31 views

### Parameter estimation using fmincon

This is a follow up to my previous question posted here. I am solving an optimization problem using fmincon in MATLAB. There are no equality constraints in my model....
118 views

### Computing the structure factor from positions and radial distribution function [closed]

I'm currently analysing some spatial point patterns that come from some fluid dynamics simulations and I'm having some difficulty computing the structure factor, $S(\pmb{k})$, from both the positions ...
I try to solve numerically the following PDE for $E(r, z)$ with a cylindrical symmetrie (i. e. $E(r, z) = E(-r, z)$). $\frac{\partial E}{\partial z} = \frac{i}{2k} \Delta E + \mathcal{N}(E)$ Where \$...