Top new questions this week:
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The algorithm for the inverse power iteration works as following : \begin{align} &v^{(0)} =\text{ some vector with }\|v^{(0)}\|=1\\ &\text{for }k = 1, 2, \ldots\\ &\qquad\text{Solve } (A – …
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The Setup Using finite differences to discretize the 2d diffusion equation $$\partial_tu=\partial_x\left(A\partial_xu+B\partial_yu\right)+\partial_y\left(B\partial_xu+C\partial_yu\right)$$ we get a …
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Assume we want to solve the Poisson eq. with the FEM on some Domain $\Omega$, i.e. $$\begin{cases} -\Delta u = f, \; \Omega\\ u = 0, \; \partial \Omega \end{cases}$$ For the sake of the discussion let …
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There exists a FFT-based method to solve the poisson equation in inhomogeneous Dirichlet boundary condition using the sine-transform. For example, Which fourier series is needed to solve a 2D poisson …
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Almost all FEM libraries are good enough, but I want to start with a FEM package and stick to it for some time. Instead of trying all of them, or going with what everyone else is using, I want to …
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Whilst googling I see reverse mode automatic differentiation (AD) tends to be used when optimising neural networks. Would it not be better to use forward mode and treat your input as a single variable,…
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Greatest hits from previous weeks:
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I want to plot a numerical integral function of some function $f$ using scipy and matplotlib. How can I do this? I tried the …
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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 …
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As I understand it, since a solution to a linear program always occurs at a vertex of its polyhedral feasible set (if a solution exists and the optimal objective function value is bounded from below, …
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Suppose $$\begin{align*} \min A &\mathrm{vec}(U) \\ &\text{subject to } U_{i,j} \leq \max\{U_{i,k}, U_{k,j}\}, \quad i,j,k = 1, \ldots, n \end{align*}$$ where $U$ is a symmetric $n\times …
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EDIT: I am testing if any eigenvalues have a magnitude of one or greater. I need to find the largest absolute eigenvalue of a large sparse, non-symmetric matrix. I have been using R’s …
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I’ve come across compression algorithms, I tried creating a simple run-length encoding algorithm but I notice that when I searched other algorithms I was shocked to know that some algorithms can …
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I am getting the warning in the post subject when attempting to optimize a function in Python with the scipy.optimize.fmin_bfgs function. The complete output: Warning: Desired error not necessarily …
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