# Tag Info

### Faster Logistic Function

Yes! There are nice approximations of the logistic. Plot of Approximating Functions As shown below, several functions approximate the logistic (shown as blue dots). This graph is available ...
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### What algorithm does (or did?) Excel use for Bessel functions that is discontinuous at x=8?

It is clear that Microsoft Excel's implementation of the BesselJ function for $N=1$ is identical to this algorithm for arguments $X < 8$: ...
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### Floating point and global error in Euler Method

In a one-step method $$y_{n+1}=y_n+h\Phi_f(x_n,y_n,h)$$ one gets a truncation error for the exact solution $$y(x_{n+1})=y(x_n)+h\Phi_f(x_n,y(x_n),h)+h^{p+1}\tau(x_n)$$ For the error propagation of ...
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### Efficiently estimating trace of a product of matrices

Edit Jan 12 I was pointed by the author of https://arxiv.org/abs/2010.09649 to this simple estimator of trace (explanation), which should also be better than the orthogonalization approach in the ...
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### Kolmogorov n-width

Given the tags of your question I believe you are refererring to the rate of decay of the singular values of a SVD performed on a snapshot matrix of a full-order model. The general (not exhaustive) ...
Accepted

### How can we calculate mixed derivatives numerically using the Chebyshev derivative matrix?

Note: Your nomenclature is only valid on Cartesian elements. If you want to calculate derivatives on arbitrary shapes you also have to consider spatial metric terms. Answer: To keep it simple, we ...
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