The use of regression analysis in the tasks of continuous monitoring of the state of systems requires a high speed of the algorithm for estimating the parameters of the model. At the same time, the estimation method must be resistant to stochastic heterogeneity of the data. This condition corresponds to the method of least modules. The paper considers one of the fastest variants of its implementation, based on the descent along the nodal straight lines. The purpose of the article is to increase the computational efficiency of the known method based on descent along nodal straight lines. The article describes an algorithm for linear regression modeling of multidimensional dynamic processes based on the least absolute deviations method. The algorithm implements gradient descent along nodal straight lines. The computational complexity of estimating regression coefficients in dynamics is reduced by using the problem solution as the starting point at the previous step. The gain is achieved by reducing the number of transitions from one node line to another. This number does not depend on the sample size. The computational complexity of the developed algorithm is estimated. A comparative analysis of the computational efficiency of the proposed and known algorithms is carried out. It is also shown that the best strategy for descending from a nodal point is to consider all nodal lines passing through this point. The developed algorithm will also improve the performance of the implementation of the generalized least absolute deviations method.