#numericalanalysis — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #numericalanalysis, aggregated by home.social.
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Start here: Standard-Slope Integration (SSI)
A new, first-of-its-kind class of derivative-driven integration operators built solely from slope information.
If you’re new to my work, this post links to the full SSI series—a structured overview of a first-of-its-kind, derivative-driven integration operator built on structural iteration invariants and slope-based reconstruction. The recap summarizes all seven posts in order and provides the conceptual foundation for understanding SSI.
Series recap:
https://mathstodon.xyz/@BlueNovaX/116523359117197532
Repository with details and examples:
https://github.com/BlueNovaX/standard-slope-integration
#numericalanalysis #scientificcomputing #mathematics #integration #StandardSlopeIntegration #SSI
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Standard‑Slope Integration (SSI) — Post #3: Failure-mode robustness
A new, first-of-its-kind class of derivative-driven integration operators built solely from slope information.
Classical integration methods often fail when the integrand is discontinuous, poorly conditioned, or structurally misaligned with area-based accumulation. SSI approaches these cases differently: its derivative-driven structure and step-to-step invariants prevent the amplification and drift that destabilize classical formulations.
This makes SSI effective in cases where traditional quadrature becomes unstable, unreliable, or fails outright—not by modifying classical methods, but by using a fundamentally different reconstruction principle.
#numericalanalysis #scientificcomputing #mathematics #integration #StandardSlopeIntegration #SSI
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An excellent introduction to #quantization used for #LLMs 👌🏽:
“Quantization From The Ground Up”, Sam Rose, Ngrok (https://ngrok.com/blog/quantization).
On HN: https://news.ycombinator.com/item?id=47519295
#AI #Math #FloatingPoint #NumericalAnalysis #Numbers #NeuralNetworks #Precision #Accuracy
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An excellent introduction to #quantization used for #LLMs 👌🏽:
“Quantization From The Ground Up”, Sam Rose, Ngrok (https://ngrok.com/blog/quantization).
On HN: https://news.ycombinator.com/item?id=47519295
#AI #Math #FloatingPoint #NumericalAnalysis #Numbers #NeuralNetworks #Precision #Accuracy
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An excellent introduction to #quantization used for #LLMs 👌🏽:
“Quantization From The Ground Up”, Sam Rose, Ngrok (https://ngrok.com/blog/quantization).
On HN: https://news.ycombinator.com/item?id=47519295
#AI #Math #FloatingPoint #NumericalAnalysis #Numbers #NeuralNetworks #Precision #Accuracy
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An excellent introduction to #quantization used for #LLMs 👌🏽:
“Quantization From The Ground Up”, Sam Rose, Ngrok (https://ngrok.com/blog/quantization).
On HN: https://news.ycombinator.com/item?id=47519295
#AI #Math #FloatingPoint #NumericalAnalysis #Numbers #NeuralNetworks #Precision #Accuracy
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`Various software efforts embrace the idea that object oriented programming enables a convenient implementation of the chain rule, facilitating so-called automatic differentiation via backpropagation. Such frameworks have no mechanism for simplifying the expressions (obtained via the chain rule) before evaluating them. As we illustrate below, the resulting errors tend to be unbounded.`
https://arxiv.org/abs/2305.03863
#calculus #software #numericalAnalysis #automaticDifferentiation #uncertainty
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🧐:
“It’s OK To Compare Floating-Points For Equality”, Nikita Lisitsa (https://lisyarus.github.io/blog/posts/its-ok-to-compare-floating-points-for-equality.html).
Via HN: https://news.ycombinator.com/item?id=47767398
On Lobsters: https://lobste.rs/s/l6c9wi/it_s_ok_compare_floating_points_for
#Math #Programming #FloatingPoint #NumericalAnalysis #Precision #Errors #Numerics
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🧐:
“It’s OK To Compare Floating-Points For Equality”, Nikita Lisitsa (https://lisyarus.github.io/blog/posts/its-ok-to-compare-floating-points-for-equality.html).
Via HN: https://news.ycombinator.com/item?id=47767398
On Lobsters: https://lobste.rs/s/l6c9wi/it_s_ok_compare_floating_points_for
#Math #Programming #FloatingPoint #NumericalAnalysis #Precision #Errors #Numerics
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🧐:
“It’s OK To Compare Floating-Points For Equality”, Nikita Lisitsa (https://lisyarus.github.io/blog/posts/its-ok-to-compare-floating-points-for-equality.html).
Via HN: https://news.ycombinator.com/item?id=47767398
On Lobsters: https://lobste.rs/s/l6c9wi/it_s_ok_compare_floating_points_for
#Math #Programming #FloatingPoint #NumericalAnalysis #Precision #Errors #Numerics
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🧐:
“It’s OK To Compare Floating-Points For Equality”, Nikita Lisitsa (https://lisyarus.github.io/blog/posts/its-ok-to-compare-floating-points-for-equality.html).
Via HN: https://news.ycombinator.com/item?id=47767398
On Lobsters: https://lobste.rs/s/l6c9wi/it_s_ok_compare_floating_points_for
#Math #Programming #FloatingPoint #NumericalAnalysis #Precision #Errors #Numerics
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Alright, future engineers!
Euler's Method: Approximates solutions to Ordinary Differential Equations (ODEs) by taking small steps along the tangent. Ex: `y_new = y_old + h * f(x_old, y_old)`. Pro-Tip: Simple, but smaller 'h' improves accuracy (at cost of computation)!
#ODEs #NumericalAnalysis #STEM #StudyNotes -
New preprint https://arxiv.org/abs/2511.06957
A #perspective discussing Moreau-Yosida (MY) techniques in #densityfunctionaltheory.
MY regularisation has enabled to import tools from #convexanalysis into #dft
providing a new mathematical understanding of the most important atomistic simulation approach
and new robust algorithms for Kohn-Sham #dft.Thanks to my co-authors from the #hylleraas centre and #oslomet for insightful discussions.
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Automatic Differentiation Can Be Incorrect
#HackerNews #AutomaticDifferentiation #Incorrectness #NumericalAnalysis #Simulation #MachineLearning
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New publication https://doi.org/10.1103/PhysRevB.111.205143
New algorithm for the #inverseproblem of Kohn-Sham #densityfunctionaltheory (#dft), i.e. to find the #potential from the #density.
Outcome of a fun collaboration of @herbst with the group of Andre Laestadius at #oslomet to derive first mathematical error bounds for this problem
#condensedmatter #planewave #numericalanalysis #convexanalysis #dftk
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Apparenty we weren't having enough issues of context collapse for #SPH as an acronym of #SmoothedParticleHydrodynamics, since I'm now seeing #STI as an acronym for #SymplecticTimeIntegrator. And of course these article are more often than not written with #LaTeX.
(No, Mastodon, I really do not want you to normalize the case of *that* tag.)
One of these I'm going to create a quiz game: #kink #fetish or #numericalAnalysis?
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I am excited to see "Splitting methods for differential equations" by Sergio Blanes, Fernando Casas and Ander Murua on arXiv: https://arxiv.org/abs/2401.01722
This is a review article to be published in the excellent Acta Numerica. It discusses numerical methods for solving differential equations which can be split in several parts that are easier to solve. In formulas, the (ordinary or partial) differential equation is 𝑑𝑢/𝑑𝑡 = 𝑓(𝑢) and the splitting is 𝑓(𝑢) = 𝑓₁(𝑢) + 𝑓₂(𝑢).
For people that don't do numerical analysis or computational mathematics, it may be helpful to think of the Lie–Trotter product formula
\[ e^{A+B} = \lim_{n\to\infty} (e^{A/n}e^{B/n})^n. \]
This is the simplest splitting method. Part of the game is to find formulas that converge faster. -
Why Death Valley Is Full Of Polygons [salt flats, deserts, and dry lakes]
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https://physics.aps.org/articles/v16/31 <-- shared article
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https://doi.org/10.1103/PhysRevX.13.011025 <-- shared paper
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#GIS #spatial #mapping #spatialanalysis #model #modeling #salt #polygons #tiling #saltflats #saltdeserts #convection #research #chemistry #water #hydrology #soil #evaporation #evapotranspiration #precipitation #solution #salinity #DeathValley #numericalanalysis #numericalmodeling #numericalsimulation #simulation #groundwater