Abstract <p>The issues of creating computationally efficient algorithms for implementing the least absolute deviation method for estimating regression dependencies have been considered. The purpose of the study is to improve the performance of gradient descent along nodal lines by considering the geometry of the objective function near the minimum as well as its comparative analysis with the gradient projection algorithm. A modified gradient descent algorithm for regression estimation using the least absolute deviation method has been proposed. Efficiency has been achieved by excluding the calculation of the objective function values in the minimums of the nodal lines and determining an improved initial approximation on part of the sample. As a result, it has been possible to reduce the dependence of computation time on sample size and expand the application area of the least absolute deviation method. The gradient projection algorithm for constructing linear regression dependencies does not guarantee finding an exact solution and is significantly inferior in performance to algorithms for descending along nodal lines.</p>