• My research group investigates the best approximation theory in Hilbert, Banach and Frechet spaces. Based on this investigations the method of least square, Ritz method, selfadjoint operators theory, spline and central (strongly optimal) algorithms theory are generalized. We use these theories for construction of a linear spline central algorithm for some ill-posed problems of computerized tomography (for inversion of Radon operator) and for some problems of quantum mechanics (for solution of equations containing multidimensional Schrodinger operator, Harmonic oscillator, creation, annihilation and numerical operators) in Hilbert space of finite n-orbits using a n-orbital operator (n=0 is a classic case). As well for construction a linear spline central and parallel algorithm for these problems in the space of all orbits, in which the problem becomes correct. Software (on C++) and numerical experiments of these tasks on the supercomputer will be implemented. As results, new mathematical models of computerized tomography with exact algorithms of its scanner, was created.