An iterative method for linear algebraic equations systems solving with positive semidefinite matrices

The normal pseudo-solution for perturbed linear algebraic equations systems with positive semidefinite matrices finding problem is considered. This problem is actual for numerical simulation process of a multibody systems dynamics taking into account additional constraints on its motion. The problem is solved by the iterative quasi-Newtonian method based on the SR1-formula for quadratic functions minimum finding. The main algorithm properties are proved. An one mechanical system dynamics study example is given, which shows the method efficiency.