Research On The Partially Randomized Extended Kaczmarz Method Of Projection Timely Updating Projection Direction

For solving large overdetermined and inconsistent system of linear equations by iteration methods,by further reconstructing the partially randomized extended Kaczmarz method proposed by Bai and Wu in 2019（PREK）.A slighted modification introduced in the involved iterative formula of partially randomized extended Kaczmarz algorithm,and obtain a projection direction timely updated partially randomized Kaczmarz method.When the coefficient matrix is assumed to be of full column rank,we prove the convergence and derive a better upper bound for the expected convergence rate of the projection direction timely updated partially randomized Kaczmarz method.The numerical results showed that the projection direction timely updated partially randomized extended Kaczmarz method can be more efficient than the partially randomized extended Kaczmarz method.