Top new questions this week:
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I need to approximate the following in $O(d)$ time for $d\times d$ diagonal $A$ and rank-1 $B$ $$u^T \exp(-A+B) v$$ Here $u,v$ are vectors in $\mathbb{R^+}^d$, $A,B$ are positive semi-definite and $B$ …
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I’m working with ODEs, $$\dot{x} = f(x, t),$$ where the (higher) derivatives of the right-hand side have discontinuities. In particular, $f(x, t)$ is obtained by interpolation of discrete samples, and …
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I am trying to solve the $\textbf{1-D}$ Poisson equation for a semiconductor structure at equilibrium (There is no external bias applied). $\textbf{Background}$ \begin{equation} \frac{d^2V}{dx^2} = -\…
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Consider a system of the following form: $$(A+K)x=b$$ where $A$ is symmetric, positive definite and block diagonal (in fact, a block diagonal matrix made of stiffness matrices arising from FEM …
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I am interested in integrals of the form $$ \int_{[0,1]^{d}} |x|^{\gamma}f(x)dx. $$ $\gamma>0$ and $f$ has some singular behavior at $\vec{0}$. The weight function $|x|^\gamma$ is commonly used in …
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Question: I am trying to solve the following PDE: $$ \begin{align*} u_{xx} + u_{yy} = \begin{cases} – \cos(x) \quad -\pi/2 \leq x \leq \pi/2, \\ 0 \quad \text{otherwise} \…
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Greatest hits from previous weeks:
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Is there a Fortran subroutine which performs linear interpolation in one-dimenional data? I need something similar to MATLAB function interp1.
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In the wave equation: $$c^2 \nabla \cdot \nabla u(x,t) – \frac{\partial^2 u(x,t)}{\partial t^2} = f(x,t)$$ Why do we first multiply by a test function $v(x,t)$ before integrating?
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I am looking for a C++ tensor library that supports dimension-agnostic code. Specifically, I need to perform operations along each dimension (up to 3), e.g. calculating a weighted sum. The dimensions …
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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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Given a positive definite symmetric matrix, what is the fastest algorithm for computing the inverse matrix and its determinant? For problems I am interested in, the matrix dimension is 30 or less. …
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There is an obvious difference between finite difference and the finite volume method (moving from point definition of the equations to integral averages over cells). But I find FEM and FVM to be very …
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Suppose I’m using a linear congruential pseudo-random number generator (PRNG). Given a seed $x_0$, the multiplying factor (a), the shift factor (c) and the modulus factor (m), how can I determine the …
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