解一类病态线性代数方程组的逐次调整消元（SAE）法

The Successive Adjustment Elimination(SAE) Method of Solving some Systems of Linear Equation with Ill-condition

In this paper,the properties of two types of matrix with ill-condi-tion are proved.Applying any linear transformation can't change the ill-condition.And a method is given,which is called Successive AdjustmentElimination(SAE)method of solving simultaneous linear equations.Theprocess of algorithm is to adjust coefficient matrix of equations based onthe right term of linear equations system successive.The purpose of adju-stment is to improve the condition of solving equations with ill-conditioncoefficient matrix.Finally,an example with ill-condition equations system is given,Theresult shows that the SAE method is efficient and for solving some linearequations system with ill-condition,is superior to the Gaussian elimina-tion algorithm in the quantity of calculation.The SAE method,therefore,is practical.