International Journal of Innovative Technology and Research
Abstract
Many problems of applications require solving of large system of equations, either under-determined, or determined, or over-determined. The equations may be subjected to constraints. The systems are typically large and sparse systems, wherein the entries of the matrix are predominantly zero. In this review article, we stress upon the applications of solving large systems arising in transmission and emission tomography. Because the measured data is typically insufficient to give a unique solution, optimization techniques such as least-squares method can be used. If the number of equations and the number of variables are small then we can solve the system using Gauss elimination method. It is quite natural in problems of applications, such as medical imaging, to encounter large system of linear equations. Thus, it is common to prefer inexact solutions over exact ones. Even when the number of equations and unknowns is large, there may not be enough information to obtain a unique solution. This is the case of over-determined system of equations and is quite normal in medical tomographic imaging, in which the images are artificially discretized approximations of parts of the interior of the body
