# Questions tagged [numerics]

Also known as Numerical Analysis, Numerics aims to provide methods and algorithms for numerical computations.

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I want to estimate the correlation parameter $\rho$ using the following expression taken from this paper (equation 10 on page 17): $$\hat{s}^2+\hat{\mu}^2=N_2(N^{-1}(\hat{\mu}),N^{-1}(\hat{\mu}), \... 2 votes 1 answer 80 views ### How to do log subtract (just like logsumexp) with probabilities? [closed] To subtract a small probability from another, this answer has constraint on log probabilities l1 > l2: Subtracting very small probabilities - How to compute? but I need a function that works for ... • 201 2 votes 1 answer 55 views ### What is a numerically stable way to generate an exponential distribution that properly yields very large, low-probability values in Excel and C++? I have sets of sampled data with the following statistics: Because the mean is so close to the min, and because of our understanding of the process that generated the samples, we are treating the ... • 331 3 votes 1 answer 4k views ### Understanding the advantages of BF16 vs. FP16 in mixed precision training Brain float (BF16) and 16-bit floating point (FP16) both require 2 bytes of memory, but in contrast to FP16, BF16 allows to represent a much larger numerical range than FP16, so under-/overflows won't ... • 151 0 votes 0 answers 37 views ### Numerical quadrature for Pareto distribution I would like to numerically evaluate an integral of the following type, when evaluating f(x) at any given point is numerically costly:$$ \int_{x_m}^\infty x^{-\alpha}f(x) \, dx, \quad \alpha >1, ...
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I've implemented the gradient descent method for finding roots of a system of nonlinear equations and I am wondering how the residual is determined? Is the residual simply the Euclidean norm (2-norm) ...
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### Approximating the standard normal density with the logistic density: How to numerically optimize $\infty$-norm?

Let's say that we want to use the logistic distribution as an approximation to the standard normal density. As the location parameter of the logistic distribution is $0$, the scale parameter $s$ is ...
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