Bi-Hamiltonian structure of the qd algorithm and new discretizations of the Toda lattice - Suris, Yuri B. (Physics letters. A, 1995)
We introduce two new discretizations of the Toda lattice related to the qd algorithm. They are demonstrated to belong to the same hierarchy as the continuous-time system, and to exemplify the general scheme for symplectic maps on Lie algebras with r-matrix Poisson brackets. The initial value problem for the difference equations is solved in terms of a factorization problem in a group. Interpolating Hamiltonian flows are found for both maps.