Syavavko M. S.
Ukr. Mat. Zh. - 2001. - 53, № 5. - pp. 662-679
We apply the method of parametrized continued fractions to the solution of systems of linear algebraic equations on the basis of their Liouville–Neumann formal power series. We construct an analog of the Cramer formula, which is also applicable to the cases of singular, ill-posed, and rectangular matrices.
Transformation of formal expansions of solutions of linear differential equations in a parameter into continued RITZ-fractions
Ukr. Mat. Zh. - 1998. - 50, № 5. - pp. 679–686
We use the apparatus of RITZ-fractions to improve the convergence of series that represent the formal solution of linear differential equations with parameter under boundary or initial conditions. We establish conditions for the existence of this solution in the case where the parameter of the equation tends to infinity. The case of a small parameter is also considered.
Ukr. Mat. Zh. - 1996. - 48, № 8. - pp. 1130-1143
We present a method for solution of linear ill-posed equations in function spaces based on the use of continuous $J$-fractions. We obtain a meromorphic solution of regularized equations and indicate some cases where a solution can be represented in terms of rational functions.
Ukr. Mat. Zh. - 1982. - 34, № 5. - pp. 559—564
Ukr. Mat. Zh. - 1974. - 26, № 6. - pp. 836–841