Least squares support vector regression for solving Volterra integral equations

被引：14

作者：

Parand, K. ^{[1
,2
,3
,4
]}

Razzaghi, M. ^{[5
]}

Sahleh, R. ^{[2
]}

Jani, M. ^{[2
]}

机构：

[1] Inst Res Fundamental Sci IPM, Sch Comp Sci, Tehran, Iran

[2] Shahid Beheshti Univ, Fac Math Sci, Dept Comp Sci, GC, Tehran, Iran

[3] Shahid Beheshti Univ, Inst Cognit & Brain Sci, Dept Cognit Modeling, GC, Tehran, Iran

[4] Univ Waterloo, Dept Stat & Actuarial Sci, Waterloo, ON, Canada

[5] Mississippi State Univ, Dept Math & Stat, Starkville, MS USA

来源：

ENGINEERING WITH COMPUTERS | 2022年 / 38卷 / SUPPL 1期

基金：

美国国家科学基金会;

关键词：

Volterra integral equations; Legendre kernel; Least squares support vector regression; Galerkin LS-SVR; Collocation LS-SVR; NUMERICAL-SOLUTION; 2ND KIND;

D O I：

10.1007/s00366-020-01186-6

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this paper, a numerical approach is proposed based on least squares support vector regression for solving Volterra integral equations of the first and second kind. The proposed method is based on using a hybrid of support vector regression with an orthogonal kernel and Galerkin and collocation spectral methods. An optimization problem is derived and transformed to solving a system of algebraic equations. The resulting system is discussed in terms of the structure of the involving matrices and the error propagation. Numerical results are presented to show the sparsity of resulting system as well as the efficiency of the method.

引用

页码：789 / 796

页数：8

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