This paper focuses on the computational efficiency of the least squares based iterative algorithms.The computational burdens of the least squares based iterative (LSI) algorithms are heavy due to computing large-size matrix inversion.In order to reduce the computational burdens,the block matrix inversion based LSI algorithms are presented.The proposed methods can reduce the computational cost through simplifying the implementation of the least squares based iterative algorithms,thus the estimation accuracies remain unchanged.The least squares based iterative algorithms and the block matrix inversion based LSI methods are studied for pseudo-linear regression systems,multivariate pseudo-linear regression systems and multivariable pseudo-linear systems.