A Method of Generalized Inverse Adjustment Based on Improved Gram-Schmidt Orthogonalization

Starting directly with coefficient matrix of condition equation or error equation,the least square solution by triangulation decomposition on coefficient matrix is carried on with improved Gram-Schmidt orthogonalization procedure.Then,the math formula and the calculation steps of solving generalized inverse matrix on improved Gram-Schmidt algorithm are deduced.The unknown solution vectors and the mathematical expression of the variance-covariance matrix are given through the generalized inverse expression.Two examples are used to verify its effect,and the results show that the modified Gram-Schmidt orthogonal method can process any matrix including rank defect array.