` Our work demonstrates the sampling of an interacting chaotic system performed on a quantum processor of ultracold atoms and opens the door of utilizable quantum computational advantage in simulating Floquet dynamics of many- body systems`
https://journals.aps.org/prx/pdf/10.1103/5mqb-3by1
#computing #quantumComputing #quantum #numericalAnalysis #science #physics
GNU Octave 11.2.0 porta ottimizzazioni, miglioramenti alla GUI e numerose correzioni per il calcolo numerico avanzato. #GNUOctave #OpenSource #Linux #ScientificComputing #NumericalAnalysis #Software
oh no! one of the greats... i still use matlab as my favorite language :)
`We are saddened to share that Cleve Moler passed away on May 20, 2026, at the age of 86 at his home surrounded by his family. Cleve was chief mathematician and cofounder of MathWorks and the author of the first version of MATLAB.`
https://www.mathworks.com/company/aboutus/founders/clevemoler.html
#CleveMoler #LinearAlgebra #software #NumericalAnalysis #MatrixComputations
Standard‑Slope Integration (SSI) — Link to Post #7: Why SSI is general-purpose
A new, first-of-its-kind class of derivative-driven integration operators built solely from slope information.
SSI is real, not a trick — it’s a general-purpose integration operator built from first principles.
Link: https://mathstodon.xyz/@BlueNovaX/116516955308646107
#numericalanalysis #scientificcomputing #mathematics #integration #StandardSlopeIntegration #SSI
Standard‑Slope Integration (SSI) — Post #7: Why SSI is general-purpose A new, first-of-its-kind class of derivative-driven integration operators built solely from slope information. Although SSI excels in difficult cases, it isn’t designed only for failures. Its derivative-driven structure and invariant-preserving iteration make it broadly applicable across smooth, irregular, and mixed-structure integrands. The same reconstruction principles that stabilize challenging cases also perform reliably in ordinary cases, giving SSI a uniquely wide operational range without unnecessary adjustments. This general-purpose behavior follows directly from SSI’s underlying structure and nothing else. #numericalanalysis #scientificcomputing #mathematics #integration #StandardSlopeIntegration #SSI
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
Standard‑Slope Integration (SSI): Series recap A new, first-of-its-kind class of derivative-driven integration operators built solely from slope information. Over the past several posts, I’ve outlined the core ideas behind Standard-Slope Integration (SSI): 1. Why derivative-driven structure matters 2. How structural iteration invariants stabilize reconstruction 3. Why SSI remains robust in cases of instability or failure 4. How slope-based reconstruction differs from area accumulation 5. How SSI diverges from classical quadrature 6. A simple example of SSI behavior 7. Why the method is genuinely general-purpose Together, these posts sketch the conceptual foundation of SSI and why it represents a new class of integration operators. More details and examples are available in the repository: https://github.com/BlueNovaX/standard-slope-integration #numericalanalysis #scientificcomputing #mathematics #integration #StandardSlopeIntegration #SSI
Standard‑Slope Integration (SSI) — Post #7: Why SSI is general-purpose
A new, first-of-its-kind class of derivative-driven integration operators built solely from slope information.
Although SSI excels in difficult cases, it isn’t designed only for failures. Its derivative-driven structure and invariant-preserving iteration make it broadly applicable across smooth, irregular, and mixed-structure integrands. The same reconstruction principles that stabilize challenging cases also perform reliably in ordinary cases, giving SSI a uniquely wide operational range without unnecessary adjustments.
This general-purpose behavior follows directly from SSI’s underlying structure and nothing else.
#numericalanalysis #scientificcomputing #mathematics #integration #StandardSlopeIntegration #SSI
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
`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
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.
🧐:
“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
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
katch wreck
Linux Easy
Peter — SSI
रञ्जित (Ranjit Mathew)
kipriyanovich