基于给定样本的概率密度近似计算函数算法中所用近似基础的选择

IF 0.4 Q4 MATHEMATICS, APPLIED

Numerical Analysis and Applications Pub Date : 2024-05-28 DOI:10.1134/s1995423924020022

A. V. Voytishek, N. Kh. Shlimbetov

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引用次数: 0

摘要

摘要在本文中，我们提出了在给定样本的基础上构建具有成本效益的近似概率密度的优化计算（数值）函数算法时选择近似基的要求，并特别关注基的稳定性和近似性。研究表明，要满足数值方案的条件优化要求并构建高效方法，最佳选择是多线性近似，以及非参数密度估计的核计算算法和投影计算算法的相应特例，即频率多边形的多维类似物。

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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Choice of Approximation Bases Used in Computational Functional Algorithms for Approximating Probability Densities on the Basis of Given Sample

Abstract

In this paper we formulate requirements for choosing approximation bases when constructing cost-effective optimized computational (numerical) functional algorithms for approximating probability densities on the basis of a given sample, with special attention paid to the stability and approximation of the bases. It is shown that to meet the requirements and construct efficient approaches to conditional optimization of numerical schemes, the best choice is a multi-linear approximation and the corresponding special case for both kernel and projection computational algorithms for nonparametric density estimation, which is a multidimensional analogue of the frequency polygon.

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来源期刊

Numerical Analysis and Applications MATHEMATICS, APPLIED-

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Numerical Analysis and Applications is the translation of Russian periodical Sibirskii Zhurnal Vychislitel’noi Matematiki (Siberian Journal of Numerical Mathematics) published by the Siberian Branch of the Russian Academy of Sciences Publishing House since 1998. The aim of this journal is to demonstrate, in concentrated form, to the Russian and International Mathematical Community the latest and most important investigations of Siberian numerical mathematicians in various scientific and engineering fields. The journal deals with the following topics: Theory and practice of computational methods, mathematical physics, and other applied fields; Mathematical models of elasticity theory, hydrodynamics, gas dynamics, and geophysics; Parallelizing of algorithms; Models and methods of bioinformatics.