Greedy randomized and maximal weighted residual Kaczmarz methods with oblique projection

<abstract><p>For solving large-scale consistent linear system, a greedy randomized Kaczmarz method with oblique projection and maximal weighted residual are proposed. By using projection, these two methods greatly reduce the number of iteration steps running time to find minimum norm solution, especially when rows matrix highly linearly correlated. Theoretical proof numerical results show that more effective than respectively.</p></abstract>