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Volume 28, Issue 2
Stability of Fredholm Integral Equation of the First Kind in Reproducing Kernel Space

Hong Du & Lihua Mu

Commun. Math. Res., 28 (2012), pp. 121-126.

Published online: 2021-05

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  • Abstract

It is well known that the problem on the stability of the solutions for Fredholm integral equation of the first kind is an ill-posed problem in $C[a, b]$ or $L^2 [a, b]$. In this paper, the representation of the solution for Fredholm integral equation of the first kind is given if it has a unique solution. The stability of the solution is proved in the reproducing kernel space, namely, the measurement errors of the experimental data cannot result in unbounded errors of the true solution. The computation of approximate solution is also stable with respect to $‖·‖_C$ or $‖· ‖_{L^2}$. A numerical experiment shows that the method given in this paper is stable in the reproducing kernel space.

  • Keywords

Freholm integral equation, ill-posed problem, reproducing kernel space.

  • AMS Subject Headings

74S30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-28-121, author = {Hong and Du and and 18472 and and Hong Du and Lihua and Mu and and 18474 and and Lihua Mu}, title = {Stability of Fredholm Integral Equation of the First Kind in Reproducing Kernel Space}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {28}, number = {2}, pages = {121--126}, abstract = {

It is well known that the problem on the stability of the solutions for Fredholm integral equation of the first kind is an ill-posed problem in $C[a, b]$ or $L^2 [a, b]$. In this paper, the representation of the solution for Fredholm integral equation of the first kind is given if it has a unique solution. The stability of the solution is proved in the reproducing kernel space, namely, the measurement errors of the experimental data cannot result in unbounded errors of the true solution. The computation of approximate solution is also stable with respect to $‖·‖_C$ or $‖· ‖_{L^2}$. A numerical experiment shows that the method given in this paper is stable in the reproducing kernel space.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19051.html} }
TY - JOUR T1 - Stability of Fredholm Integral Equation of the First Kind in Reproducing Kernel Space AU - Du , Hong AU - Mu , Lihua JO - Communications in Mathematical Research VL - 2 SP - 121 EP - 126 PY - 2021 DA - 2021/05 SN - 28 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19051.html KW - Freholm integral equation, ill-posed problem, reproducing kernel space. AB -

It is well known that the problem on the stability of the solutions for Fredholm integral equation of the first kind is an ill-posed problem in $C[a, b]$ or $L^2 [a, b]$. In this paper, the representation of the solution for Fredholm integral equation of the first kind is given if it has a unique solution. The stability of the solution is proved in the reproducing kernel space, namely, the measurement errors of the experimental data cannot result in unbounded errors of the true solution. The computation of approximate solution is also stable with respect to $‖·‖_C$ or $‖· ‖_{L^2}$. A numerical experiment shows that the method given in this paper is stable in the reproducing kernel space.

Hong Du & Lihua Mu. (2021). Stability of Fredholm Integral Equation of the First Kind in Reproducing Kernel Space. Communications in Mathematical Research . 28 (2). 121-126. doi:
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