"Application of multiprocessor systems to solving the two-dimensional convolution-type Fredholm integral equations of the first kind for vector-functions"
Evdokimova N.A., Lukyanenko D.V., Yagola A.G.

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

Evdokimova N.A.   e-mail: naevdok@math.susu.ac.ru;
Lukyanenko D.V.   e-mail: lukyanenko-dmitry@yandex.ru;   Yagola A.G.   e-mail: yagola@yahoo.com