Let I be a monic generalized Jacobi matrix, i.e. a three-diagonal block matrix of special form, introduced by M. Derevyagin and V. Derkach in 2004. We find conditions for a monic generalized Jacobi matrix I to admit a factorization I = LU with L and U being lower and upper triangular two-diagonal block matrices of special form. In this case the Darboux transformation of I defined by I<^>p = UL is shown to be also a monic generalized Jacobi matrix. Analogues of Christoffel formulas for polynomials of the first and the second kind, corresponding to the Darboux transformation I<^>p are found.

With each sequence of real numbers <$Es~=~left {s sub j right } sub j=0 sup inf> two kinds of continued fractions are associated, - the so-called P-fraction and a generalized Stieltjes fraction that, in the case when <$Es~=~left {s sub j right } sub j=0 sup inf> is a sequence of moments of a probability measure on <$E{ roman bold R} sub +>, coincide with the J-fraction and the Stieltjes fraction, respectively. A subclass H<^>reg of regular sequences is specified for which explicit formulas connecting these two continued fractions are found. For <$Es~symbol <174>~H sup reg> the Darboux transformation of the corresponding generalized Jacobi matrix is calculated in terms of the generalized Stieltjes fraction.