url stringlengths 31 38 | title stringlengths 7 229 | abstract stringlengths 44 2.87k | text stringlengths 319 2.51M | meta dict |
|---|---|---|---|---|
https://arxiv.org/abs/2105.10615 | Convergence directions of the randomized Gauss--Seidel method and its extension | The randomized Gauss--Seidel method and its extension have attracted much attention recently and their convergence rates have been considered extensively. However, the convergence rates are usually determined by upper bounds, which cannot fully reflect the actual convergence. In this paper, we make a detailed analysis ... | \section{Introduction}
Linear least squares problem is a ubiquitous problem arising frequently in data analysis and scientific computing. Specifically, given a data matrix $A\in R^{m\times n}$ and a data vector $b\in R^{m}$, a linear least squares problem can be written as follows
\begin{equation}
\label{ls}
\min \limi... | {
"timestamp": "2021-05-25T02:05:27",
"yymm": "2105",
"arxiv_id": "2105.10615",
"language": "en",
"url": "https://arxiv.org/abs/2105.10615",
"abstract": "The randomized Gauss--Seidel method and its extension have attracted much attention recently and their convergence rates have been considered extensively.... |
https://arxiv.org/abs/1912.01763 | A note on semi-infinite program bounding methods | Semi-infinite programs are a class of mathematical optimization problems with a finite number of decision variables and infinite constraints. As shown by Blankenship and Falk (Blankenship and Falk. "Infinitely constrained optimization problems." Journal of Optimization Theory and Applications 19.2 (1976): 261-281.), a ... |
\section{Introduction}
This note discusses methods for the global solution of semi-infinite programs (SIP).
Specifically, the method from \cite{mitsos11} is considered, and it is shown with a counterexample that the lower bounds do not always converge.
Throughout we use notation as close as possible to that used in \c... | {
"timestamp": "2019-12-05T02:06:35",
"yymm": "1912",
"arxiv_id": "1912.01763",
"language": "en",
"url": "https://arxiv.org/abs/1912.01763",
"abstract": "Semi-infinite programs are a class of mathematical optimization problems with a finite number of decision variables and infinite constraints. As shown by ... |
https://arxiv.org/abs/math/0610707 | A fixed point theorem for the infinite-dimensional simplex | We define the infinite dimensional simplex to be the closure of the convex hull of the standard basis vectors in R^infinity, and prove that this space has the 'fixed point property': any continuous function from the space into itself has a fixed point. Our proof is constructive, in the sense that it can be used to find... | \section{Introduction}
In finite dimensions, one of the simplest methods for proving the
Brouwer fixed point theorem is via a combinatorial result known as
Sperner's lemma \cite{Sper28}, which is a statement about labelled
triangulations of a simplex in $\ensuremath{\mathbb{R}} ^n$. In this paper, we use
Sperner's le... | {
"timestamp": "2006-10-24T03:10:17",
"yymm": "0610",
"arxiv_id": "math/0610707",
"language": "en",
"url": "https://arxiv.org/abs/math/0610707",
"abstract": "We define the infinite dimensional simplex to be the closure of the convex hull of the standard basis vectors in R^infinity, and prove that this space... |
https://arxiv.org/abs/1911.12009 | Involution pipe dreams | "Involution Schubert polynomials represent cohomology classes of $K$-orbit closures in the complete (...TRUNCATED) | "\\section{Introduction}\n\nOne can identify the equivariant cohomology rings for the spaces of symm(...TRUNCATED) | {"timestamp":"2020-08-17T02:05:50","yymm":"1911","arxiv_id":"1911.12009","language":"en","url":"http(...TRUNCATED) |
https://arxiv.org/abs/1410.6535 | A New Fractional Derivative with Classical Properties | "We introduce a new fractional derivative which obeys classical properties including: linearity, pro(...TRUNCATED) | "\\section{Introduction}\nThe derivative of non-integer order has been an interesting research topic(...TRUNCATED) | {"timestamp":"2014-11-11T02:08:51","yymm":"1410","arxiv_id":"1410.6535","language":"en","url":"https(...TRUNCATED) |
https://arxiv.org/abs/2204.00383 | A visualisation for conveying the dynamics of iterative eigenvalue algorithms over PSD matrices | "We propose a new way of visualising the dynamics of iterative eigenvalue algorithms such as the QR (...TRUNCATED) | "\\section{Simple iterative eigenvalue algorithms}\n\nThe (naive) QR algorithm {\\cite{francis1961qr(...TRUNCATED) | {"timestamp":"2022-04-04T02:21:37","yymm":"2204","arxiv_id":"2204.00383","language":"en","url":"http(...TRUNCATED) |
https://arxiv.org/abs/2010.15204 | Shortest closed curve to inspect a sphere | "We show that in Euclidean 3-space any closed curve which lies outside the unit sphere and contains (...TRUNCATED) | "\\section{Introduction}\nWhat is the shortest closed orbit a satellite may take to inspect the en(...TRUNCATED) | {"timestamp":"2021-07-23T02:04:13","yymm":"2010","arxiv_id":"2010.15204","language":"en","url":"http(...TRUNCATED) |
https://arxiv.org/abs/2107.02428 | Browder's Theorem through Brouwer's Fixed Point Theorem | "One of the conclusions of Browder (1960) is a parametric version of Brouwer's Fixed Point Theorem, (...TRUNCATED) | "\\section{Introduction}\r\n\r\nBrouwer's Fixed Point Theorem (Hadamard, 1910, Brouwer, 1911) states(...TRUNCATED) | {"timestamp":"2021-07-07T02:12:17","yymm":"2107","arxiv_id":"2107.02428","language":"en","url":"http(...TRUNCATED) |
https://arxiv.org/abs/2107.14079 | Density of binary disc packings: lower and upper bounds | "We provide, for any $r\\in (0,1)$, lower and upper bounds on the maximal density of a packing in th(...TRUNCATED) | "\\section{Introduction}\n\nA {\\em disc packing} (or {\\em circle packing}) is a set of interior-di(...TRUNCATED) | {"timestamp":"2022-06-07T02:28:12","yymm":"2107","arxiv_id":"2107.14079","language":"en","url":"http(...TRUNCATED) |
https://arxiv.org/abs/math/0411020 | Resolutions of small sets of fat points | "We investigate the minimal graded free resolutions of ideals of at most n+1 fat points in general p(...TRUNCATED) | "\\section[1]{Introduction}\\label{s:intro}\n\nThe study of sets of fat points in projective space i(...TRUNCATED) | {"timestamp":"2005-06-01T19:10:15","yymm":"0411","arxiv_id":"math/0411020","language":"en","url":"ht(...TRUNCATED) |
End of preview. Expand in Data Studio
Top ranking subsets of https://huggingface.co/datasets/math-ai/AutoMathText with additional filters (see notebook in repo root)
configs
from pprint import pprint
from datasets import get_dataset_config_names
def fetch_and_print_configs(dataset_name):
"""helper fn to print configs"""
configs = get_dataset_config_names(dataset_name)
print(f"Available configurations for dataset '{dataset_name}':")
pprint(configs, width=80, compact=True)
ds_name = "BEE-spoke-data/AutoMathText-top-hf"
fetch_and_print_configs(ds_name)
Available configurations for dataset 'BEE-spoke-data/AutoMathText-top-hf': ['code-python-0.70-to-1.00', 'code-python-0.80-to-1.00', 'default', 'web-0.70-to-1.00', 'web-0.80-to-1.00']
- the
defailtconfig is filteredarxiv-0.80-to-1.00
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