First thing we need to do is try our best to define the quantum of separation for bfloat16. Rigorously, this is the minimum Chebyshev distance between two vectors that makes them distinguishable. Math math math, and the answer I have is 3.051758e-5 distance units. So not that small!
November 7, 2025 at 6:09 PM
First thing we need to do is try our best to define the quantum of separation for bfloat16. Rigorously, this is the minimum Chebyshev distance between two vectors that makes them distinguishable. Math math math, and the answer I have is 3.051758e-5 distance units. So not that small!
Then, by power of fiat, we double that value to get 3.051758e-05 distance units. That's the minimum Chebyshev distance, at this scale, that guarantees two values will end up distinguishable. Any less than that and it's not a sure thing.
November 7, 2025 at 6:09 PM
Then, by power of fiat, we double that value to get 3.051758e-05 distance units. That's the minimum Chebyshev distance, at this scale, that guarantees two values will end up distinguishable. Any less than that and it's not a sure thing.
The whole subject of "classical orthogonal polynomials" appears repeatedly in physics, but usually isn't studied in its own right. We end up having to look up whether a certain polynomial is Hermite, or Legendre, or Chebyshev, or whatever. (At least I do.)
en.wikipedia.org/wiki/Classic...
en.wikipedia.org/wiki/Classic...
Classical orthogonal polynomials - Wikipedia
en.wikipedia.org
October 24, 2025 at 3:13 PM
The whole subject of "classical orthogonal polynomials" appears repeatedly in physics, but usually isn't studied in its own right. We end up having to look up whether a certain polynomial is Hermite, or Legendre, or Chebyshev, or whatever. (At least I do.)
en.wikipedia.org/wiki/Classic...
en.wikipedia.org/wiki/Classic...
In addition to dapper looks and exceptional mathematical ability, Pafnuty Chebyshev has a stamp in his honor. His four-bar linkage is depicted on the middle left, but I can't make out the significance of the integral depicted in the upper left. Anyone know what it means? 🧮
![Russian stamp commemorating Chebyshev (1821-1894). An integral in the upper left says
\int x^m (ax^n + b)^p dx
m,n,p rational, a,b in [can't make out]
Why is it on the stamp?](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:ysaiuavm2f7d4th42c4valhw/bafkreih5hphq3goj22mv4furoo2qupepmj5zetzdexyixnyls44cjixw4u@jpeg)
September 24, 2025 at 11:49 PM
In addition to dapper looks and exceptional mathematical ability, Pafnuty Chebyshev has a stamp in his honor. His four-bar linkage is depicted on the middle left, but I can't make out the significance of the integral depicted in the upper left. Anyone know what it means? 🧮
Erik Parkinson, Kate Wall, Jane Slagle, Daniel Treuhaft, Xander de la Bruere, Samuel Goldrup, Timothy Keith, Peter Call, Tyler J. Jarvis
Chebyshev Subdivision and Reduction Methods for Solving Multivariable Systems of Equations
https://arxiv.org/abs/2401.02114
Chebyshev Subdivision and Reduction Methods for Solving Multivariable Systems of Equations
https://arxiv.org/abs/2401.02114
October 28, 2024 at 5:00 AM
Erik Parkinson, Kate Wall, Jane Slagle, Daniel Treuhaft, Xander de la Bruere, Samuel Goldrup, Timothy Keith, Peter Call, Tyler J. Jarvis
Chebyshev Subdivision and Reduction Methods for Solving Multivariable Systems of Equations
https://arxiv.org/abs/2401.02114
Chebyshev Subdivision and Reduction Methods for Solving Multivariable Systems of Equations
https://arxiv.org/abs/2401.02114
New post: Posthumous Chebyshev Polynomials
https://www.johndcook.com/blog/2025/02/12/chebyshev-third-fourth/
https://www.johndcook.com/blog/2025/02/12/chebyshev-third-fourth/
February 12, 2025 at 12:25 PM
New post: Posthumous Chebyshev Polynomials
https://www.johndcook.com/blog/2025/02/12/chebyshev-third-fourth/
https://www.johndcook.com/blog/2025/02/12/chebyshev-third-fourth/
La tendencia #BTCUSD definida por los polinomios de Chebyshev pronostica un rango de precio de US$111,600 el 16 de enero de 2025.
#bitcoin #tradingstrategy #inversión #cryptocurrencies
#bitcoin #tradingstrategy #inversión #cryptocurrencies
January 6, 2025 at 5:27 AM
La tendencia #BTCUSD definida por los polinomios de Chebyshev pronostica un rango de precio de US$111,600 el 16 de enero de 2025.
#bitcoin #tradingstrategy #inversión #cryptocurrencies
#bitcoin #tradingstrategy #inversión #cryptocurrencies
ordered Banach space. We explore the fundamental properties of best approximations in this setting, such as the best approximation sets and the Chebyshev sets. [2/2 of https://arxiv.org/abs/2503.10137v1]
March 14, 2025 at 6:03 AM
ordered Banach space. We explore the fundamental properties of best approximations in this setting, such as the best approximation sets and the Chebyshev sets. [2/2 of https://arxiv.org/abs/2503.10137v1]
The discussion touched upon specific examples like Chebyshev polynomials, illustrating how orthogonal polynomials are applied in numerical methods related to integration. #ApproximationTheory 6/6
June 9, 2025 at 3:00 AM
The discussion touched upon specific examples like Chebyshev polynomials, illustrating how orthogonal polynomials are applied in numerical methods related to integration. #ApproximationTheory 6/6
🔄 Updated Arxiv Paper
Title: Chebyshev centers and radii for sets induced by quadratic matrix inequalities
Authors: Amir Shakouri, Henk J. van Waarde, M. Kanat Camlibel
Read more: https://arxiv.org/abs/2403.05315
Title: Chebyshev centers and radii for sets induced by quadratic matrix inequalities
Authors: Amir Shakouri, Henk J. van Waarde, M. Kanat Camlibel
Read more: https://arxiv.org/abs/2403.05315
October 21, 2025 at 8:16 AM
🔄 Updated Arxiv Paper
Title: Chebyshev centers and radii for sets induced by quadratic matrix inequalities
Authors: Amir Shakouri, Henk J. van Waarde, M. Kanat Camlibel
Read more: https://arxiv.org/abs/2403.05315
Title: Chebyshev centers and radii for sets induced by quadratic matrix inequalities
Authors: Amir Shakouri, Henk J. van Waarde, M. Kanat Camlibel
Read more: https://arxiv.org/abs/2403.05315
arXiv:2503.12403v1 Announce Type: new
Abstract: This paper investigates the potential applications of a parametric family of polynomial wavelets that has been recently introduced starting from de la Vall\'ee Poussin (VP) interpolation at Chebyshev [1/4 of https://arxiv.org/abs/2503.12403v1]
Abstract: This paper investigates the potential applications of a parametric family of polynomial wavelets that has been recently introduced starting from de la Vall\'ee Poussin (VP) interpolation at Chebyshev [1/4 of https://arxiv.org/abs/2503.12403v1]
March 18, 2025 at 6:04 AM
arXiv:2503.12403v1 Announce Type: new
Abstract: This paper investigates the potential applications of a parametric family of polynomial wavelets that has been recently introduced starting from de la Vall\'ee Poussin (VP) interpolation at Chebyshev [1/4 of https://arxiv.org/abs/2503.12403v1]
Abstract: This paper investigates the potential applications of a parametric family of polynomial wavelets that has been recently introduced starting from de la Vall\'ee Poussin (VP) interpolation at Chebyshev [1/4 of https://arxiv.org/abs/2503.12403v1]
Boris Faleichik, Andrew Moisa: Explicit Runge-Kutta-Chebyshev methods of second order with monotonic stability polynomial https://arxiv.org/abs/2504.00323 https://arxiv.org/pdf/2504.00323 https://arxiv.org/html/2504.00323
April 2, 2025 at 6:04 AM
Boris Faleichik, Andrew Moisa: Explicit Runge-Kutta-Chebyshev methods of second order with monotonic stability polynomial https://arxiv.org/abs/2504.00323 https://arxiv.org/pdf/2504.00323 https://arxiv.org/html/2504.00323
coherent regions. GeloVec combines modified Chebyshev distance metrics with multispatial transformations to enhance segmentation accuracy through stabilized feature extraction. The core innovation lies in the adaptive sampling weights system that [3/8 of https://arxiv.org/abs/2505.01057v1]
May 5, 2025 at 6:00 AM
coherent regions. GeloVec combines modified Chebyshev distance metrics with multispatial transformations to enhance segmentation accuracy through stabilized feature extraction. The core innovation lies in the adaptive sampling weights system that [3/8 of https://arxiv.org/abs/2505.01057v1]
Researchers derived formulas showing Chebyshev coefficients shrink proportionally to powers of the interval length L as it narrows, with a fixed number of nodes. Read more: https://getnews.me/chebyshev-coefficient-decay-on-tiny-intervals-and-quadrature-impact/ #chebyshev #spectralmethods
September 19, 2025 at 8:58 PM
Researchers derived formulas showing Chebyshev coefficients shrink proportionally to powers of the interval length L as it narrows, with a fixed number of nodes. Read more: https://getnews.me/chebyshev-coefficient-decay-on-tiny-intervals-and-quadrature-impact/ #chebyshev #spectralmethods
my arch-nemesis used to be Chebyshev
October 6, 2025 at 9:30 PM
my arch-nemesis used to be Chebyshev
Leokadia Bialas-Ciez, Dimitri Jordan Kenne, Alvise Sommariva, Marco Vianello
Chebyshev admissible meshes and Lebesgue constants of complex polynomial projections. (arXiv:2311.06511v1 [math.NA])
http://arxiv.org/abs/2311.06511
Chebyshev admissible meshes and Lebesgue constants of complex polynomial projections. (arXiv:2311.06511v1 [math.NA])
http://arxiv.org/abs/2311.06511
November 14, 2023 at 4:02 AM
Leokadia Bialas-Ciez, Dimitri Jordan Kenne, Alvise Sommariva, Marco Vianello
Chebyshev admissible meshes and Lebesgue constants of complex polynomial projections. (arXiv:2311.06511v1 [math.NA])
http://arxiv.org/abs/2311.06511
Chebyshev admissible meshes and Lebesgue constants of complex polynomial projections. (arXiv:2311.06511v1 [math.NA])
http://arxiv.org/abs/2311.06511
🔄 Updated Arxiv Paper
Title: Least multivariate Chebyshev polynomials on diagonally determined domains
Authors: Mareike Dressler, Simon Foucart, Mioara Joldes, Etienne de Klerk, Jean-Bernard Lasserre, Yuan Xu
Read more: https://arxiv.org/abs/2405.19219
Title: Least multivariate Chebyshev polynomials on diagonally determined domains
Authors: Mareike Dressler, Simon Foucart, Mioara Joldes, Etienne de Klerk, Jean-Bernard Lasserre, Yuan Xu
Read more: https://arxiv.org/abs/2405.19219
December 19, 2024 at 8:03 AM
🔄 Updated Arxiv Paper
Title: Least multivariate Chebyshev polynomials on diagonally determined domains
Authors: Mareike Dressler, Simon Foucart, Mioara Joldes, Etienne de Klerk, Jean-Bernard Lasserre, Yuan Xu
Read more: https://arxiv.org/abs/2405.19219
Title: Least multivariate Chebyshev polynomials on diagonally determined domains
Authors: Mareike Dressler, Simon Foucart, Mioara Joldes, Etienne de Klerk, Jean-Bernard Lasserre, Yuan Xu
Read more: https://arxiv.org/abs/2405.19219
Chebyshev多項式のまとまった解説が欲しいな〜
February 11, 2024 at 1:02 PM
Chebyshev多項式のまとまった解説が欲しいな〜
Saeed Tafazolia, Jaap Top: CM theory, maximal hyperelliptic curves, and Chebyshev polynomials https://arxiv.org/abs/2509.00273 https://arxiv.org/pdf/2509.00273 https://arxiv.org/html/2509.00273
September 3, 2025 at 6:39 AM
Saeed Tafazolia, Jaap Top: CM theory, maximal hyperelliptic curves, and Chebyshev polynomials https://arxiv.org/abs/2509.00273 https://arxiv.org/pdf/2509.00273 https://arxiv.org/html/2509.00273
Improvement: Paketti Chebyshev Polynomial Waveshaper Dialog will now update to the next instrument or sample if you select a new instrument or a new sample. Also tweaked the Dialog around and optimized
#paketti #tracker #patreon #lua #renoise #demoscene #trackermusic
#paketti #tracker #patreon #lua #renoise #demoscene #trackermusic
October 22, 2025 at 11:28 PM
Improvement: Paketti Chebyshev Polynomial Waveshaper Dialog will now update to the next instrument or sample if you select a new instrument or a new sample. Also tweaked the Dialog around and optimized
#paketti #tracker #patreon #lua #renoise #demoscene #trackermusic
#paketti #tracker #patreon #lua #renoise #demoscene #trackermusic
Philos. Trans. R. Soc. A: Partial Chebyshev polynomials and fan graphs
https://royalsocietypublishing.org/doi/abs/10.1098/rsta.2024.0417?af=R
https://royalsocietypublishing.org/doi/abs/10.1098/rsta.2024.0417?af=R
October 16, 2025 at 2:10 PM
Philos. Trans. R. Soc. A: Partial Chebyshev polynomials and fan graphs
https://royalsocietypublishing.org/doi/abs/10.1098/rsta.2024.0417?af=R
https://royalsocietypublishing.org/doi/abs/10.1098/rsta.2024.0417?af=R
Observe also that this is not a purely univariate-multivariate thing; note that Chebyshev polynomials remain a useful thing to know about for e.g. numerical integration of dynamical systems in high dimension.
October 21, 2025 at 8:43 AM
Observe also that this is not a purely univariate-multivariate thing; note that Chebyshev polynomials remain a useful thing to know about for e.g. numerical integration of dynamical systems in high dimension.
Manhattan geometry lesbians and Chebyshev distance gays
November 14, 2025 at 7:11 PM
Manhattan geometry lesbians and Chebyshev distance gays
Chebyshev Polynomials in the 16th Century (2022)
Chebyshev polynomials in the 16th century
We give a few examples of Chebyshev polynomials that appeared in mathematical problems from the 16th and 17th century. The main example is the famous equation of Adrianus Romanus (Adriaan van Roomen)...
arxiv.org
November 27, 2024 at 7:37 PM
Chebyshev Polynomials in the 16th Century (2022)
3/ Novel Approach
I extend hyperboloidal slicing and spectral methods from a scalar toy model to full gravitational perturbations in the Lorenz gauge. These methods allow for compactified domain calculations that efficiently span the entire spacetime.
I extend hyperboloidal slicing and spectral methods from a scalar toy model to full gravitational perturbations in the Lorenz gauge. These methods allow for compactified domain calculations that efficiently span the entire spacetime.
November 25, 2024 at 4:35 PM
3/ Novel Approach
I extend hyperboloidal slicing and spectral methods from a scalar toy model to full gravitational perturbations in the Lorenz gauge. These methods allow for compactified domain calculations that efficiently span the entire spacetime.
I extend hyperboloidal slicing and spectral methods from a scalar toy model to full gravitational perturbations in the Lorenz gauge. These methods allow for compactified domain calculations that efficiently span the entire spacetime.