Kovalchuk O. Algorithms for Systems with Toeplitz lambda-Matrices and their Application

Candidate of Phys. & Math Sci. Degree Thesis. Speciality 01.05.02 - Mathematical Modelling and Computation Methods. V.M.Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, 2005. In the thesis new effective algorithms of solution of system of linear algebraic equations with Hankel matrices and Toeplitz matrices with polynomical and trigonometrical elements for the first time are developed. Parallel and consecutive models of systems of the linear algebraic equations with block-Toeplitz matrices solving are constructed. For the received algorithms the return analysis of errors of rounding off has been made. It is as a result established, that computer realization of methods for Toeplitz matrices correspond the limited equivalent indignations which at the use of a mode ад ( ) for scalar products do not depend on the system's order. On the basis of the developed computing algorithms with use of means of object-oriented programming the program is created. Computing experiments which confirm efficiency of the offered computing schemes are made. The developed algorithms are introduced into the educational process of the I.Ya.Horbachevsky Ternopil State Medical University in the form of programs. Keywords: -matrices, Toeplitz matrices, Hankel matrices, algebraic polynom, trigonometrical polynom, round error, branched continued fraction, parallel models, block algorithm.