Top new questions this week:
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I have a cubic lattice $L_1\times L_2 \times L_3$ with the periodic boundary condition. I have to construct the Laplacian matrix in the sparse format. My matlab code is like this …
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I meet a problem when I try to develop an iterative method for discrete inverse problem $$Ax+e=b$$ where $A\in\mathbb{R}^{m\times n}$ and $e$ is a noise. I want to approximate the true solution $x_{…
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I am looking to compute the derivative of the following expression: $$\frac{\partial}{\partial X}\mathrm{tr}\left[A\exp(X)\right]$$ where $A$ is both a symmetrical and positive-definite matrix and $X$ …
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For the sake of the rest of the question, I’m interested in the porous medium equation $$S\frac{\partial\phi}{\partial t} = \nabla\cdot K\phi\,\nabla\phi$$ where $S$ and $K$ are spatially-variable …
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Consider the following linear PDE: $$\nabla_q V(q) – M_d(q)M^{-1}(q)\nabla_q V_d(q) = 0,$$ where $V(q)$ and $M(q)$ are known and $M_d(q)$ is a grey box function (e.x., $M_d(q)$ is fitted using a …
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I try to detect interference fringes in a bunch of pictures. I projected on one axis, and I was able to detekt the peaks that indicate one of the fringes. So now I’m having a list with points (e.g. $(…
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I am trying to numerically integrate a differential equation using scipy.integrate.RK45 and/or scipy.integrate.LSODA. Now, I am trying to fix the integration step sizes of both solvers. This, however, …
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Greatest hits from previous weeks:
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In this comment I wrote: …default SciPy integrator, which I’m assuming only uses symplectic methods. in which I am refering to SciPy’s odeint, which uses …
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Fortran has a special place in numerical programming. You can certainly make good and fast software in other languages, but Fortran keeps performing very well despite its age. Moreover, it’s easier to …
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I am used to thinking of finite-differences as a special case of finite-elements, on a very constrained grid. So what are the conditions on how to choose between Finite Difference Method (FDM) and …
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What considerations should I be making when choosing between BFGS and conjugate gradient for optimization? The function I am trying to fit with these variables are exponential functions; however, the …
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In FEM classes, it’s usually taken for granted that the stiffness matrix is positive definite, but I just can’t understand why. Could anyone give some explanation? For instance, we can consider 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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Right now I stuck with a problem. It seems to be really trivial one, but still it is hard for me to find an appropriate solution. The problem is: One has two intervals and are to find the intersection …
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