Geodesic
A method of restoring the aerosol particle size distribution function on the set of piecewise-convex functions
Numerical methods and programming, Tome 13 (2012) no. 1, pp. 49-66

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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.
Keywords: aerosol particle size distribution function; Fredholm integral equations of the first-kind; conjugate gradient projection method; piecewise-convex functions. 
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     author = {Y. Wang and Y. Zhang and D. V. Luk'yanenko and A. G. Yagola},
     title = {A method of restoring the aerosol particle size distribution function on the set of piecewise-convex functions},
     journal = {Numerical methods and programming},
     pages = {49--66},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2012_13_1_a7/}
}
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Y. Wang; Y. Zhang; D. V. Luk'yanenko; A. G. Yagola. A method of restoring the aerosol particle size distribution function on the set of piecewise-convex functions. Numerical methods and programming, Tome 13 (2012) no. 1, pp. 49-66. http://geodesic.mathdoc.fr/item/VMP_2012_13_1_a7/