A method of restoring the aerosol particle size distribution function on the set of piecewise-convex functions



aerosol particle size distribution function, Fredholm integral equations of the first-kind, conjugate gradient projection method, piecewise-convex functions


The problem of restoring the aerosol particle size distribution function with the use of the measured particle extinction spectrum is considered. This problem is reduced to a Fredholm integral equation of the first-kind. The conjugate gradient method with the projection on a constraint set is applied as a minimization process of the residual functional. The constraints are chosen as piecewise-convex functions on the basis of physical features of the sought solution. An efficient scheme of regularization for the problems of such a type is proposed. This work was partially supported by the Russian Foundation for Basic Research (projects os. 11-01-00040 and 10-01-91150-NFSC).

Author Biographies

Y. Wang

Institute of Geology and Geophysics, Chinese Academy of Sciences
Beitucheng Western Road, 19, 100029, Beijing, China
• Professor

D.V. Lukyanenko

A.G. Yagola

Y. Zhang

Institute of Geology and Geophysics, Chinese Academy of Sciences
Beitucheng Western Road, 19, 100029, Beijing, China
• PhD Student


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How to Cite

Ван Я., Лукьяненко Д.В., Ягола А.Г., Чжан Е. A Method of Restoring the Aerosol Particle Size Distribution Function on the Set of Piecewise-Convex Functions // Numerical methods and programming. 2012. 13. 49-66



Section 1. Numerical methods and applications

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