基于支持向量机的离散线性微分方程求解方法

王丹荣; 莫艳

doi:10.12052/gdutxb.190050

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基于支持向量机的离散线性微分方程求解方法

综合研究 | 更新时间：2026-05-27

- 基于支持向量机的离散线性微分方程求解方法
- Support Vector Machines Based Method to Solve Discrete Linear Differential Equations
- 广东工业大学学报 2020年37卷第2期页码：87-93
- 作者机构：
  
  广东工业大学应用数学学院,广东,广州,510520
- 作者简介：
  
  王丹荣(1991–)，女，硕士研究生，主要研究方向为计算及应用调和分析
  莫艳(1986–)，女，副教授，主要研究方向为计算及应用调和分析，E-mail：marvel-2008@163.com
- 基金信息：
  
  国家自然科学基金资助项目(11801095，11626067);广东省自然科学基金资助项目(2017A030310538);广东省高校特色创新项目(2017KTSCX062);广东工业大学青年百人科研启动基金资助项目(220413131，220413550)
- DOI：10.12052/gdutxb.190050
  中图分类号： O172.1
- 网络首发：2020-03-10，
  
  纸质出版：2020
- 稿件说明：
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王丹荣, 莫艳. 基于支持向量机的离散线性微分方程求解方法[J]. 广东工业大学学报, 2020, 37(2): 87-93.

Wang Dan-rong, Mo Yan. Support Vector Machines Based Method to Solve Discrete Linear Differential Equations[J]. 2020, 37(2): 87-93.
王丹荣, 莫艳. 基于支持向量机的离散线性微分方程求解方法[J]. 广东工业大学学报, 2020, 37(2): 87-93. DOI： 10.12052/gdutxb.190050.

Wang Dan-rong, Mo Yan. Support Vector Machines Based Method to Solve Discrete Linear Differential Equations[J]. 2020, 37(2): 87-93. DOI： 10.12052/gdutxb.190050.

摘要

支持向量机(Support Vector Machines

SVMs)在逼近问题的求解上展现出了良好的有效性和可行性

而微分方程求解问题是许多学者研究的热门课题。其中

离散微分方程及其逆问题的求解具有十分重要的意义。本文将支持向量机、Tikhonov正则化和再生核理论相结合

提出一种求解离散线性微分方程及其逆问题的方法。该方法适用于一般的离散线性微分方程及其逆问题的求解，能够得到具有解析表达式的稀疏解

便于后续应用。实验表明

所提出的方法是有效的。

Abstract

Support vector machines (SVMs) show excellent effectiveness and feasibility in solving approximation problems. Solving differential equations is a hot topic studied by many scholars

in which the solutions of discrete differential equations and their inverse problems are of great significance. A method of solving discrete linear differential equations and their inverse problems is proposed by combining support vector machines

Tikhonov regularization and the theory of reproducing kernels. This method is suitable for solving general discrete linear differential equations and their inverse problems. This method can obtain sparse solutions with analytical expressions

which is convenient for subsequent applications. Experiments show that the proposed method is effective.

关键词

Keywords

references

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