Geodesic
Application of multiprocessor systems to solving the two-dimensional convolution-type Fredholm integral equations of the first kind for vector-functions
Numerical methods and programming, Tome 10 (2009) no. 2, pp. 263-267

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Some features of numerical solving the convolution-type Fredholm integral equations of the first kind for vector-functions with the use of multiprocessor systems are considered. The Tikhonov regularization is applied for solving this ill-posed problem. The Tikhonov functional's extremal is found using the two-dimensional discrete Fourier transform. The choice of the regularization parameter is performed according to the generalized discrepancy principle. Several parallelization schemes are proposed to solve this problem; the efficiency of these schemes is shown.
Keywords: inverse problem; equation of convolution type; vector function; mathematical simulation; Tikhonov regularization; parallel algorithms. 
@article{VMP_2009_10_2_a8,
     author = {N. A. Evdokimova and D. V. Luk'yanenko and A. G. Yagola},
     title = {Application of multiprocessor systems to solving the two-dimensional convolution-type {Fredholm} integral equations of the first kind for vector-functions},
     journal = {Numerical methods and programming},
     pages = {263--267},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2009_10_2_a8/}
}
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N. A. Evdokimova; D. V. Luk'yanenko; A. G. Yagola. Application of multiprocessor systems to solving the two-dimensional convolution-type Fredholm integral equations of the first kind for vector-functions. Numerical methods and programming, Tome 10 (2009) no. 2, pp. 263-267. http://geodesic.mathdoc.fr/item/VMP_2009_10_2_a8/