Geodesic
Some regularizing algorithms for the solution of integral equations of the first kind with a priori restrictions
Matematičeskoe modelirovanie, Tome 4 (1992) no. 4, pp. 89-100 Cet article a éte moissonné depuis la source Math-Net.Ru

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An approach to the construction of regularizing algorithms is considered in the problem of finding a stable approximate solution of the operator equation $Au=f$, where $A$ is a continuous operator from $C[a,b]$ to a normed linear space $F$, when there are a priori restrictions on the exact solution $u(x)$. The method is numerically implemented for the solution of Volterra integral equations and Fredholm integral equations of the first kind, when there is a priori information of various types. The algorithm is realized in the form of a program for IBM PC AT. In the finite-dimensional approximation the irregular grids for the right-hand side, the kernel and the desired solution of the equation are used. Such grids are useful in application of the algorithm to specific practical problems. 
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     author = {V. P. Zagonov and S. V. Podolyako},
     title = {Some regularizing algorithms for the solution of integral equations of the first kind with a~priori restrictions},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {89--100},
     year = {1992},
     volume = {4},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1992_4_4_a8/}
}
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V. P. Zagonov; S. V. Podolyako. Some regularizing algorithms for the solution of integral equations of the first kind with a priori restrictions. Matematičeskoe modelirovanie, Tome 4 (1992) no. 4, pp. 89-100. http://geodesic.mathdoc.fr/item/MM_1992_4_4_a8/