Application of iterative method in linear equations

Iterative method is one of the basic tools of data analysis and is widely used in many fields. This paper introduces the history of the least squares method, and discusses the basic theories and several common variable fitting methods with an iterative approach. The first method is linear fitting, which is used to fit a straight line; the simplest and most important linear fitting is that through origin. The second is curve fitting; through the conversion of curvilinear equation to linear equation or multivariate linear equation, linear fitting is achieved iteratively. The third is multivariable linear fitting, which involves multiple linear regressions where one variable is statistically influenced by many factors. This paper compares these different methods and defines how to choose the optimal curve fitting when using the iterative method in linear fitting. On this basis, the paper addresses several problems when using the iterative method: losing necessary variables, qualitative differences in explanatory variable, introducing unnecessary explanatory variable, and linearization error in nonlinear equations.