Incomplete givens orthogonalization based on Bi-down dating

Abstract

In this paper we present incomplete Givens orthogonalization technique(IGOT) based on bi-down dating techniques which zero-out entries based on the structure of interest(upper or lower triangular),the incomplete Cholesky factor(upper triangular factor) is used as a preconditioner for the normal equation of the least squares problem. This approach shows that Givens rotations satisfy the characteristics of incomplete QR factorization and due to it simplicity it is more computationally simple when compared to pre-processing method. The solution to the least squares problem is obtained without necessarily forming the normal equation rather the approach utilizes the triangular structure.