#approximation — Public Fediverse posts

#approximation : a drawing, advancing or being near

- French: approximation

- German: die Annäherung

- Italian: ravvicinamento

- Portuguese: aproximação

- Spanish: aproximación

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

Try our new word guessing game @ https://24hippos.com

Trapezoidal Rule: Estimates definite integrals by approximating the area under a curve with trapezoids. Ex: For one interval, Area ≈ h/2 * (f(a) + f(b)). Pro-Tip: Smaller step sizes (more trapezoids) = significantly better accuracy! #NumericalIntegration #Approximation #STEM #StudyNotes

#BusyBusyBusy... #BusyBeingChinese...

#Quote: 不是高帆,是看不见的风。

The #PSiBoRG is #Coming...

#ComingSoon; #DrPSiReN is #WatchingYou...

🧙:Polymaths:​🤖:wolfparty:🤖:Polymaths:​🧙 | :fediverse:​🦹:PirateBadge:🦄:PirateBadge:🦹:fediverse:

#AlsoBeingEuropean #Approximation #LiteraryTranslations #AIInTheWild #NotBeenInvented #TheIndustrialGoldenAge #CyborgOrangeJesus

#BusyBusyBusy... #BusyBeingChinese...

#Quote: 不是高帆,是看不见的风。

The #PSiBoRG is #Coming...

#ComingSoon; #DrPSiReN is #WatchingYou...

🧙:Polymaths:​🤖:wolfparty:🤖:Polymaths:​🧙 | :fediverse:​🦹:PirateBadge:🦄:PirateBadge:🦹:fediverse:

#AlsoBeingEuropean #Approximation #LiteraryTranslations #AIInTheWild #NotBeenInvented #TheIndustrialGoldenAge #CyborgOrangeJesus

#approximation : a drawing, advancing or being near

- French: approximation

- German: die Annäherung

- Italian: ravvicinamento

- Portuguese: aproximação

- Spanish: aproximación

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

Try our new word guessing game @ https://24hippos.com

In the thrilling new world of #Lean4, we've finally proven bounds for the Randomized MaxCut #Approximation algorithm that nobody asked for. 📈🔍 Now you can confidently cut those graphs like a pro while impressing... well, nobody. Because who doesn't love an NP-Complete problem just chilling with some approximation algorithms? 🙄🎉
https://abhamra.com/blog/randomized-maxcut/ #RandomizedMaxCut #NPComplete #Algorithms #GraphTheory #HackerNews #ngated

In the thrilling new world of #Lean4, we've finally proven bounds for the Randomized MaxCut #Approximation algorithm that nobody asked for. 📈🔍 Now you can confidently cut those graphs like a pro while impressing... well, nobody. Because who doesn't love an NP-Complete problem just chilling with some approximation algorithms? 🙄🎉
https://abhamra.com/blog/randomized-maxcut/ #RandomizedMaxCut #NPComplete #Algorithms #GraphTheory #HackerNews #ngated

In the thrilling new world of #Lean4, we've finally proven bounds for the Randomized MaxCut #Approximation algorithm that nobody asked for. 📈🔍 Now you can confidently cut those graphs like a pro while impressing... well, nobody. Because who doesn't love an NP-Complete problem just chilling with some approximation algorithms? 🙄🎉
https://abhamra.com/blog/randomized-maxcut/ #RandomizedMaxCut #NPComplete #Algorithms #GraphTheory #HackerNews #ngated

In the thrilling new world of #Lean4, we've finally proven bounds for the Randomized MaxCut #Approximation algorithm that nobody asked for. 📈🔍 Now you can confidently cut those graphs like a pro while impressing... well, nobody. Because who doesn't love an NP-Complete problem just chilling with some approximation algorithms? 🙄🎉
https://abhamra.com/blog/randomized-maxcut/ #RandomizedMaxCut #NPComplete #Algorithms #GraphTheory #HackerNews #ngated

mistakes were made, who needs perfect symetry anyway?

#bartop #arcade #fermi #approximation

#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

Правда ли KAN лучше MLP? Свойство разделения глубины между двумя архитектурами

Прошлым летом в свет вышла новая архитектура нейронных сетей под названием Kolmogorov-Arnold Networks (KAN). На момент выхода статьи про KAN эта новость произвела фурор в мире машинного обучение, так как KAN показывала существенный прирост в качестве аппроксимации различных сложных функций. Ошибка новых сетей падает значительно быстрее при увеличении числа параметров. Однако, за все приходится платить, и цена таких маленьких значений функции ошибки - медленное обучение: KAN обучается примерно в 10 раз медленнее, чем старый добрый MLP. Из всего этого возникает вопрос: насколько все же уместно использование новой архитектуры вместо привычных всем MLP? В данной статье будет найдена функция, которая может быть реализована с помощью двухслойного KAN полиномиальной ширины, но не может быть приближена никакой двухслойной ReLU MLP сетью с полиномиальной шириной

https://habr.com/ru/articles/929972/

#kan #mlp #approximation #math #machine_learning #deep_learning #science #neural_networks #research

Pi Approximation Day (22/7) actually is on 21.9911485751286 / 7 = 07-21T23:47:15.237...

#Pi #Approximation #Day #PiApproximationDay

#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

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

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

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

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

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

https://gist.github.com/Marc-B-Reynolds/9fb24a7a4ee915e6e973bf9f4d08c404

#FloatingPoint #Approximation #Sqrt

Comparison of basic 1/sqrt implementations. Short versions. Next is a version by Carlos F. Borges' which is correctly rounded except for 1 value per 2 power-of-two intervals (1 per 2 exponent values...like [1,4])

Test driver (& references to Borge) are in this gist: https://gist.github.com/Marc-B-Reynolds/9fb24a7a4ee915e6e973bf9f4d08c404

The driver also includes:
• 1/sqrt(x) - which I had forget to include.
• correctly rounded versions
• SSE rsqrt approx
• old skool quake approx (added a modernized one)

#FloatingPoint #Approximation #Sqrt

Finally the most sophisticated of the three is Simpson’s rule in which pairs of adjacent strips use a #quadratic #parabola to interpolate between the ordinates. This even better at convergence than the trapezium rule. I’ve shown a different function here because for the function shown above the difference between the approximation and the numerical #approximation is not discernible.

#MyWork #Mathematics #Maths #Numerics #SimpsonsRule #FreeSoftware #CCBYSA #Wikipedia #Wikimedia

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/

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

Misleading GPS, Philosophy of Maps, And You - The oft-quoted saying “all models are wrong, but some are useful” is a tounge-in-c... - https://hackaday.com/2024/09/10/misleading-gps-philosophy-of-maps-and-you/ #approximation #precision #gpshacks #accuracy #mapping #garmin #strava #model #gps #map

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

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

'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.`

https://link.springer.com/chapter/10.1007/978-3-031-11818-0_59

Updated: reciprocal approximation gist to add the new variant presented by Mike Day (paper link in C-source)

https://gist.github.com/Marc-B-Reynolds/bab0efc00c55be52f8663a762131ada2

#FloatingPoint #Approximation

I've found a decent working approximation of π for #PostScript

/pi 0.001 sin 2 div 360000 mul def

Accurate to 7 decimal places. The language uses single-precision floating point, and all its trig routines work in degrees.

This calculates π using the area of a unit radius n-gon, with n=360000

A = ½n⋅sin(360°÷n)

One of Ramanujan's approximations

π ≅ 9801÷(2206⋅√2)

is about as accurate but opaque.

#mathematics #pi #approximation #FloatingPoint

Exploring the Approximation Capabilities of Multiplicative Neural Networks for Smooth Functions

Ido Ben-Shaul, Tomer Galanti, Shai Dekel

Action editor: Murat Erdogdu.

https://openreview.net/forum?id=sWQJfb2GSk

#neurons #layers #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

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

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

Finally the most sophisticated of the three is Simpson’s rule in which pairs of adjacent strips use a #quadratic #parabola to interpolate between the ordinates. This even better at convergence than the trapezium rule. I’ve shown a different function here because for the function shown above the difference between the approximation and the numerical #approximation is not discernible.

#MyWork #Mathematics #Maths #Numerics #SimpsonsRule #FreeSoftware #CCBYSA #Wikipedia #Wikimedia

#CO2 #approximation #climate #ClimateChange #klima #klimakrise #Klimawandel

Ich habe nochmal versucht, die #KeelingKurve zu approximieren. Ist mir gelungen.

Erschreckend, wie gut die Approximation ist und wie stabil die CO₂-Konzentration ansteigt.

Anfang 2000 hätte der Wert für April 2023 auf 2,83 ppm genau vorhergesagt können – und wäre unterschätzt worden.

BTW: Neben der jährlichen Oszillation gibt es seltsamerweise eine schwächere, halbjährliche Oszillation.

https://byggvir.de/2023/05/16/approximating-monthly-data-of-the-keeling-curve-of-atmospheric-co2-concentration-using-exponential-and-sinusoidal-functions/

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/

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/

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/

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/