Lmst

#approximation : a drawing, advancing or being near

- French: approximation

- German: die Annäherung

- Italian: ravvicinamento

- Portuguese: aproximação

- Spanish: aproximación

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Word of The Hour's Annual Survey @ https://wordofthehour.org/r/form

It is well known that the "spherical cow" is an overly aggressive approximation. Hence:

https://arxiv.org/abs/2504.00506

#spherical #cow #approximation

用「加法」來計算浮點數乘法的近似值

在「Why Does Integer Addition Approximate Float Multiplication? (probablydance.com)」這邊看到的，原文在「Why Does Integer Addition Approximate Float Mu

https://blog.gslin.org/archives/2025/02/16/12265/%e7%94%a8%e3%80%8c%e5%8a%a0%e6%b3%95%e3%80%8d%e4%be%86%e8%a8%88%e7%ae%97%e6%b5%ae%e9%bb%9e%e6%95%b8%e4%b9%98%e6%b3%95%e7%9a%84%e8%bf%91%e4%bc%bc%e5%80%bc/

#Murmuring #754 #addition #approximate #approximation #float #ieee #integer #multiplication

Previously mentioned Hastings 1955 #approximation and remembered I have #sollya files for some. This is the first few atan approximations.

I'm sharing because it's an example of using a "seed" approximation to refine the coefficients using sollya. In these cases sollya would fail to converge without the seed. Other examples are using some other tool (say multiprecision or CAS) to get a first pass.

https://gist.github.com/Marc-B-Reynolds/450cec7f3646314c88a353bde50273d1

'Zeroth-order Stochastic Approximation Algorithms for DR-submodular Optimization', by Yuefang Lian, Xiao Wang, Dachuan Xu, Zhongrui Zhao.

http://jmlr.org/papers/v25/23-1523.html

#approximation #optimization #algorithms

#approximation : a drawing, advancing or being near

- French: approximation

- German: die Annäherung

- Italian: ravvicinamento

- Portuguese: aproximação

- Spanish: aproximación

------------

Word of The Hour's Annual Survey @ https://wordofthehour.org/r/form

Misleading GPS, Philosophy of Maps, And You https://hackaday.com/2024/09/10/misleading-gps-philosophy-of-maps-and-you/ #approximation #precision #gpshacks #accuracy #mapping #garmin #Strava #model #gps #map

Physics heresy: Projectiles don’t actually make parabolas

Taught in every introductory physics class for centuries, the parabola is only an imperfect approximation of the true path of a projectile. #Projectile #Projectiles #ProjectileMotion #Parabola #Approximation #Physics #Heresy #Parabolas

https://bigthink.com/starts-with-a-bang/projectiles-dont-make-parabolas/

Today is 22/7: Happy π-approximation-day!

#pi #approximation #day #pi22dividedby7
#donchonk #catsofmastodon

Donnie in a box, hard at work to get more likes and reposts.

11/X
Mme la Présidente reprend la parole et, chose inhabituelle, répond en direct à M. Platret concernant ses propos accusateurs concernant la gestion des Fonds Européens. 🇪🇺

"M. Platret, M. Platret, mais de quels chiffres parlez-vous? Par pitié, pourriez-vous entrer concrètement dans le sujet? De quoi parlez vous, de la JDA, du PDR Bourgogne, des 14 plans mobilisés par la Région? Nous avions la semaine dernière 4h et de mi de réunion très apaisées avec la Chambre Régionale de l'Agriculture. De quoi parlez-vous? Sortez de votre joute oratoire pour venir dans le sujet!"

#CriseAgricole
#Approximation

'Kernel Thinning', by Raaz Dwivedi, Lester Mackey.

http://jmlr.org/papers/v25/21-1334.html

#kernels #approximation #kernel

The following formula yields the correct decimal digits of π up to 42 quadrillion digits. Also, see the general form. This high-precision approximation is related to the properties of theta functions or the Gaussian integral.

#pi #digits #quadrillion #quadrilliondigits #GaussianIntegral #ThetaFunction #Maths #Formula #Approximation

Flattening Bézier Curves and Arcs
https://minus-ze.ro/posts/flattening-bezier-curves-and-arcs/
#ycombinator #graphics #vector_graphics #flattening #approximation #Bézier #quadratic #cubic #elliptical #arcs #blossom #De_Casteljau #subdivision #arc_length #path_length

'Limitations on approximation by deep and shallow neural networks', by Guergana Petrova, Przemyslaw Wojtaszczyk.

http://jmlr.org/papers/v24/22-1381.html

#approximation #lipschitz #approximants

Cazabon's #Film #Quality #Approximation:

The overall quality and #watchability of a film can be approximated with the following #equation:

Q = 1 / ((n - 2) ^ 2)

... where Q is `watchability` in the interval [0, 1], and `n` is the number of genres the movie is categorized as having in its IMDB listing.

Action, Comedy: 1.0
Drama, Thriller, Music: 1.0
Action, Comedy, Drama, Horror, Thriller: 0.111

Note: there's a discontinuity at n == 2, which we avoid by using the value `1` in that case.

1/2

`The solution of this SDE lies on the manifold of symmetric and positive semi-definite matrices, so structure-preserving schemes are needed for its numerical #approximation. We apply #stochastic Lie group methods based on Runge-Kutta–Munthe-Kaas schemes for ODEs to guarantee that the numerical solution evolves on the correct #manifold. We also present an application example to illustrate our methodology.`