Pershyna I. The theory of discontinuous splines and its application in сomputer tomography

Thesis is devoted to the development of the theory of approximation of discontinuous functions discontinuous linear splines and its application to the solution of two-dimensional problem of computed tomography and 3D and 4D mathematical modeling in computer tomography using blending approximation of functions of three variables by Bernstein polynomials. The results, which are an extension of the theory of approximation of discontinuous functions discontinuous functions; together are a further generalization and development of the theory of approximation of functions by operators of mixed approximation; is the basis of a common approach to mathematical modeling and problem solving two-dimensional, three-dimensional and four-dimensional computed tomography. A method for the search of points and lines of discontinuity of one or two variables with the help of its approach discontinuous linear interpolation, approximation and interlination spline using rektangulation domain of the functions (in the case of two variables). Developed 3D and 4D mathematical models and methods of recovery of stationary and dynamic three-dimensional internal structure of the body from its tomograms (projections) that lie in the mutually perpendicular planes using the blending approximation of functions of three variables by Bernstein polynomials.