Семинар за рачунарство и примењену математику, 18. октобар 2016.

Наредни састанак Семинара биће одржан у уторак, 18. октобра 2016. у сали 301ф Математичког института САНУ са почетком у 14:15 часова.

Предавач: Марко Петковић, Природно-математички факултет у Нишу

Наслов предавања: ITERATIVE METHODS FOR COMPUTING GENERALIZED INVERSES

Апстракт: We consider the class of iterative methods for computing generalized inverses $A^{(2)}_{\mathcal{R}(G),\mathcal{N}(G)}$, given by $X_{k+1}=X_k p(AX_k)$ where $p$ is polynomial. These methods generalize well-known hyper-power methods of order $r$, obtained by taking $p(x)=1+x+\ldots+x^{r-1}$. We examine the convergence properties and convergence order of these methods, depending on the polynomial $p(x)$. Moreover, we give the methods with highest possible convergence order, taking a certain number of matrix multiplications per iteration. These results can be efficiently used to improve several methods for finding 1-norm minimal solution of the linear system and have various applications, including image deblurring and compressed sensing.