SOLUTION OF ALGEBRAIC EQUATIONS BY THE METHOD OF АITKEN-NIKIPORTS - Gennadiy Anatol'yevich Kirichenko; Vladimir Vasil'yevich Selyankin; Vladimir Ilyich Shmoylov (Наука. Инновации. Технологии, 2022)
Presents analytical expressions representing all the roots of a random algebraic equation of the n-th degree through the ratio of the original equation. These formulas consist of two relations infnite Toeplitz determinants, diagonal elements of which are the coef-fcients of the algebraic equation. Such structures were called continuous fractions of Nikip-ortsa. For effcient calculation of the values of continued fractions of Nikiportsa used recurrent algorithm of Rutishauser. When fnding the roots of a polynomial algorithm for the summation of divergent continued fractions ( r/φ -algorithm). Complex roots are determined from consider-ation of the values of a long series of suitable continuous fractions. As an example, consider the solution of the algebraic equation 25-th degree.