半代数集的持久同调

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Applied Algebra and Geometry Pub Date : 2023-09-27 DOI:10.1137/22m1494415

Saugata Basu, Negin Karisani

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引用次数: 4

摘要

本文给出了一种单指数复杂度的算法，用于计算给定多项式的子水平集对给定半代数集的过滤达到(任意固定)维的条形码。我们的算法是第一个解决单指数复杂性问题的算法，并推广了计算无过滤半代数集到维数的Betti数的相应结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Persistent Homology of Semialgebraic Sets

We give an algorithm with singly exponential complexity for computing the barcodes up to dimension (for any fixed ) of the filtration of a given semialgebraic set by the sublevel sets of a given polynomial. Our algorithm is the first algorithm for this problem with singly exponential complexity and generalizes the corresponding results for computing the Betti numbers up to dimension of semialgebraic sets with no filtration present.

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来源期刊

SIAM Journal on Applied Algebra and Geometry MATHEMATICS, APPLIED-

CiteScore

2.20

自引率

0.00%

发文量