计算随机地图静态密度的二次样条投影法

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-01 DOI:10.4310/cms.2024.v22.n2.a9

Azzah Alshekhi, Jiu Ding, Noah Rhee

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引用次数: 0

摘要

我们提出了一种二次样条线投影法，可以计算随机映射的静态密度，其概率与位置有关。利用相应马尔可夫算子的关键变化不等式，我们证明了由拉索塔-约克类区间图组成的随机图族的数值方案的规范收敛性。数值实验结果表明，与之前基于算子逼近的随机地图数值方法相比，新方法改善了$L^1$正则误差，大大提高了收敛速度。

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A quadratic spline projection method for computing stationary densities of random maps

We propose a quadratic spline projection method that computes stationary densities of random maps with position-dependent probabilities. Using a key variation inequality for the corresponding Markov operator, we prove the norm convergence of the numerical scheme for a family of random maps consisting of the Lasota–Yorke class of interval maps. The numerical experimental results show that the new method improves the $L^1$-norm errors and increases the convergence rate greatly, compared with the previous operator-approximation-based numerical methods for random maps.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.