ABS algorithm;  projection matrix;  Search vector

On the basis of the basic ABS algorithm, a class of vector-type ABS algorithm for solving large sparse problems is presented by using the characteristics of the ABS algorithm, which overcomes the shortcomings of the large amount of operation and storage caused by the modified projection matrix in the original ABS algorithm, and discusses the convergence and stability of the algorithm. Experiments show that the algorithm has the characteristics of fast convergence speed, high calculation accuracy, small amount of operation and small amount of storage.