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Computation of a functional for large values

Consider the following function : $$f(x) = \sin^2(\frac{π\Gamma(x)}{2x})$$ Now consider the following functional : $$I(x)=\int_0^\infty \frac{f(x + iy) − f(x − iy)}{e^{2πy}-1} dy$$ I need values for ...
3k views

Quality of eigenvalue approximation in Lanczos method

I try to familiarize myself with iterative eigenvalue solvers such as Lanczos. So I tried rewrite it to python directly according to wiki. But it doesn't seem to work. The problem: it approximates ...
10 views

Python programming [closed]

Cannon Ball Simulation Add a new class named "Cannon". This class it to represent the cannon that launches the balls. It should draw a rectangle the launch point. Its width should be equal ...
46 views

Calculate stable time step DG method for advection-diffusion

For stable time steps for the RKDG method for transport equations we require that $$\Delta t \le \frac{\Delta x CFL}{(2k + 1)|\lambda|},$$ where $\lambda$ is the eigenvalue of our conservation law ...
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Scipy minimization failing with inequality constraints or bounds

I am trying to use scipy.optimize to solve a minimizaiton problem but getting failures on using an inequality constraint or a bound. Looking for any suggestions regarding proper usage of constraints ...
119 views

How to define a dimensionless Objective function for determining how peaked a curve is?

I have attached 2 plots for FFT spectra. One is considered good and one is bad. The good one is classified on the basis of how closely spaced the frequencies and the bad is based on how multiple ...
62 views

Efficient projection of a vector onto matrix kernel

Given an $m \times n$ matrix $A$ and a vector $x\in\mathbb R^n$, with $m<n$, what's an efficient way of computing the projection of $x$ onto the kernel of $A$?
32 views

Surface mesh from labeled 3D points

I'm trying to figure out how to create a surface mesh from a set of labeled 3D points. The 3D object could be something like part of a cave system or asteroid where there would be parts of the surface ...
355 views

How to implement flexible gmres in matlab?

About the flexible GMRES (fgmres), we know that it is a variant of right preconditioned gmres. And the robust command gmres in matlab as follows: ...
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Sufficient conditions to ensure divergence of a sequence in Maxima

I am using Maxima to check whether a given sequence is diverging to $+\infty$. I know that this problem is undecidable and we note that Maxima is throwing an error: ...
33 views

Linear system with an l1-norm constraint

I have a saddle-point system of the form \begin{bmatrix} A & B \\ B^T & O \end{bmatrix}\begin{bmatrix} x\\ y \end{bmatrix} = \begin{bmatrix} f \\ \vec{0} \end{bmatrix}, \end{...
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Differences between Discrete Fourier Transform and Continuous Fourier Transform?

I am trying to visualize the time dependence of a free particle given an initial wave-function using Python and I just wanted to know if I could use the in built FFT implementation from NumPy to find ...
26 views

How to create a simulated federated learning network to study sybil attacks?

I'm trying to study the relationship, if any, between the accuracy of a federated learning network and the number of attacking sybils. In order to do this, I need to create a simulated FL network and ...
72 views

Is Romberg integration method implemented as weighted function values numerically correct?

I have to integrate expression f(x) * g(x) for many different functions f but just one g. I ...
377 views

General case Kutta condition

I'm working on a 2D inviscid fluid simulation using a "panel method", with Potential being used to enforce the no-through boundary condition. I'm trying to incorporate the Kutta condition, which says ...
The following relates to the linked question: Scattering of waves in a symmetrical potential (using python) I have attempted to solve the problem for $U(r)$ using ...