Geodesic
On matrix decomposition of one reduced cubic irrational
Čebyševskij sbornik, Tome 14 (2013) no. 1, pp. 34-55.

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In this work we considered the matrix decomposition of the cubic irrational $\alpha$ satisfying the equation $$x^3 - 4x^2 - 5x - 1 = 0.$$ For decomposition of the matrix $$ \left( \begin{array}{c} \alpha \\ 1 \\ \end{array} \right)=\prod_{k=0}^\infty\left( \begin{array}{cc} 310941\cdot k+155427 156744\cdot k+78333 \\ 61578\cdot k+30882 31041\cdot k+15564\\ \end{array} \right) $$ an algorithm of transition to regular continued fraction is constructed. Bibliography: 2 titles.
Keywords: continued fraction, matrix decomposition, reduced cubic irrational, algorithm of transition from matrix decomposition to continued fraction. 
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N. M. Dobrovol'skii; D. K. Sobolev; V. N. Soboleva. On matrix decomposition of one reduced cubic irrational. Čebyševskij sbornik, Tome 14 (2013) no. 1, pp. 34-55. http://geodesic.mathdoc.fr/item/CHEB_2013_14_1_a3/

[1] Podsypanin V. D., “O razlozhenii irratsionalnostei chetvertoi stepeni v nepreryvnuyu drob”, Chebyshevskii sbornik, 8:3(23) (2007), 43–46 | Zbl

[2] Podsypanin E. V., “O razlozhenii irratsionalnostei vysshikh stepenei v obobschennuyu nepreryvnuyu drob (po materialam V. D. Podsypanina, rukopis 1970)”, Chebyshevskii sbornik, 8:3(23) (2007), 47–49 | Zbl