Summation of Poincaré theta series in the Schottky model

New algorithms for approximate summation of linear Poincaré theta series in the Schottky model of real hyperelliptic curves are proposed. As a result, for the same output accuracy estimate, the amount of computations is reduced by several times in the case of slow convergence and by tens of percent in the usual situations. For the sum of the Poincaré series over the subtree on descendants of a given node, a new estimate in terms of the series member at this node is obtained.