The Least Squares Solution of Large Overdetermined Linear Equations

Xinxue Jiang

Shiyuan College, Nanning Normal University, Nanning, 530226, China

Abstract: Because the least squares solutions of large overdetermined linear equations have large relative er-rors, the least squares solutions of large overdetermined linear equations are studied. Firstly, according to the matrix characteristic analysis of large overdetermined linear equations, the equations are transformed and calculated. Then PCA was used as the theoretical basis to decompose and calculate the large-scale overdeter-mined linear equations, and the error of the calculation results was calculated to obtain the estimated value with the minimum error. Finally, the dimensionality of the estimated value is reduced to complete the non-negative treatment of the solution value, and the processed value is output as the least squares solution, thus realizing the calculation of the least squares solution of the large overdetermined linear equations. The expe-rimental results show that the relative error of the proposed method is less than that of the traditional method, and it can meet the precision requirement of the least square solution of the large overdetermined linear equations.

Keywords: Overdetermined linear equations; Least squares solution; Relative error; Nonnegative treatment