A convergence rate for approximate solutions of Fredholm integral equations of the first kind

Shaobo Lin; Feilong Cao; Zongben Xu

doi:10.1007/s11117-011-0137-5

A convergence rate for approximate solutions of Fredholm integral equations of the first kind

Shaobo Lin
, Feilong Cao
, Zongben Xu

China Jiliang University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We study the convergence rate for solving Fredholm integral equations of the first kind by using the well known collocation method. By constructing an approximate interpolation neural network, we deduce the convergence rate of the approximate solution by only using continuous functions as basis functions for the Fredholm integral equations of the first kind. This convergence rate is bounded in terms of a modulus of smoothness.

Original language	English
Pages (from-to)	641-652
Number of pages	12
Journal	Positivity
Volume	16
Issue number	4
DOIs	https://doi.org/10.1007/s11117-011-0137-5
State	Published - Dec 2012

Keywords

Approximate solution
Convergence rate
Fredholm integral equations

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10.1007/s11117-011-0137-5

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title = "A convergence rate for approximate solutions of Fredholm integral equations of the first kind",

abstract = "We study the convergence rate for solving Fredholm integral equations of the first kind by using the well known collocation method. By constructing an approximate interpolation neural network, we deduce the convergence rate of the approximate solution by only using continuous functions as basis functions for the Fredholm integral equations of the first kind. This convergence rate is bounded in terms of a modulus of smoothness.",

keywords = "Approximate solution, Convergence rate, Fredholm integral equations",

author = "Shaobo Lin and Feilong Cao and Zongben Xu",

year = "2012",

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doi = "10.1007/s11117-011-0137-5",

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T1 - A convergence rate for approximate solutions of Fredholm integral equations of the first kind

AU - Lin, Shaobo

AU - Cao, Feilong

AU - Xu, Zongben

PY - 2012/12

Y1 - 2012/12

N2 - We study the convergence rate for solving Fredholm integral equations of the first kind by using the well known collocation method. By constructing an approximate interpolation neural network, we deduce the convergence rate of the approximate solution by only using continuous functions as basis functions for the Fredholm integral equations of the first kind. This convergence rate is bounded in terms of a modulus of smoothness.

AB - We study the convergence rate for solving Fredholm integral equations of the first kind by using the well known collocation method. By constructing an approximate interpolation neural network, we deduce the convergence rate of the approximate solution by only using continuous functions as basis functions for the Fredholm integral equations of the first kind. This convergence rate is bounded in terms of a modulus of smoothness.

KW - Approximate solution

KW - Convergence rate

KW - Fredholm integral equations

UR - https://www.scopus.com/pages/publications/84869109306

U2 - 10.1007/s11117-011-0137-5

DO - 10.1007/s11117-011-0137-5

M3 - 文章

AN - SCOPUS:84869109306

SN - 1385-1292

VL - 16

SP - 641

EP - 652

JO - Positivity

JF - Positivity

IS - 4

ER -

A convergence rate for approximate solutions of Fredholm integral equations of the first kind

Abstract

Keywords

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