Journal of Applied Mathematics

Semidefinite Optimization Providing Guaranteed Bounds on Linear Functionals of Solutions of Linear Integral Equations with Smooth Kernels

Guangming Zhou, Chao Deng, and Kun Wu

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Abstract

Based on recent progress on moment problems, semidefinite optimization approach is proposed for estimating upper and lower bounds on linear functionals defined on solutions of linear integral equations with smooth kernels. The approach is also suitable for linear integrodifferential equations with smooth kernels. Firstly, the primal problem with smooth kernel is converted to a series of approximative problems with Taylor polynomials obtained by expanding the smooth kernel. Secondly, two semidefinite programs (SDPs) are constructed for every approximative problem. Thirdly, upper and lower bounds on related functionals are gotten by applying SeDuMi 1.1R3 to solve the two SDPs. Finally, upper and lower bounds series obtained by solving two SDPs, respectively infinitely approach the exact value of discussed functional as approximative order of the smooth kernel increases. Numerical results show that the proposed approach is effective for the discussed problems.

Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 340567, 8 pages.

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305574

Digital Object Identifier
doi:10.1155/2014/340567

Mathematical Reviews number (MathSciNet)
MR3178957

Zentralblatt MATH identifier
07010604

Citation

Zhou, Guangming; Deng, Chao; Wu, Kun. Semidefinite Optimization Providing Guaranteed Bounds on Linear Functionals of Solutions of Linear Integral Equations with Smooth Kernels. J. Appl. Math. 2014 (2014), Article ID 340567, 8 pages. doi:10.1155/2014/340567. https://projecteuclid.org/euclid.jam/1425305574


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