Earlier we computed the Klein’s polyhedral for two cubic forms of Davenport g₁ and g₂. Now we take one 3-dimensional vector L for each of g₁ and g₂. For this vector L compute expansion giving by algorithms of Euler, Jacobi, Poincare, Brun and by two new algorithms. We consider the position of the computed integer approximations Ρĸ to the ray λL with respect to the Klein’s polyhedral. We study the periods of the algorithms as well. From this point of view we estimate a quality of each algorithm. It was found that only algorithms of Euler, Jacobi and Bruno are good enough.

Mathematical problems and theory of numerical methods

Bruno Alexander Dmitrievich,  abruno@keldysh.ru,  orcid.org/0000-0002-7465-1258,  KIAM RAS

Parusnikov V. I.,  parus@keldysh.ru,  KIAM RAS