Solving the polynomial approximation problem with use of the iterative kachmazh method

In this work, we describe a classical iterative Kachmazh method and a modification thereof using a relaxation parameter. We study at which rate the Kachmazh method with a relaxation parameter converges when applied to solving a least squares problem of large dimension. Recommendations are given for choosing the relaxation parameter in a particular case - when solving the problem of polynomial approximation of the experimental data in the least squares sense.