CAJ | 학술논문

针对绝对值方程Ax＋B x=b的求解问题,给出了光滑牛顿法。通过引进极大熵函数将绝对值方程进行光滑化处理,进而转化为非线性光滑方程组,利用光滑牛顿算法对其进行求解,并对算法的收敛性和收敛速度进行了验证。数值实验结果表明该算法是有效的。
침대절대치방정Ax＋B x=b적구해문제,급출료광활우돈법。통과인진겁대적함수장절대치방정진행광활화처리,진이전화위비선성광활방정조,이용광활우돈산법대기진행구해,병대산법적수렴성화수렴속도진행료험증。수치실험결과표명해산법시유효적。
Aimed at the solution to the absolute value equation Ax＋Bx=b,this paper presents a smooth Newton method.By using the maximum entropy function,absolute value equations problem could be transformed into the nonlinear smooth equations.Then the smooth Newton method is proposed for solving the absolute value equations and its convergence and convergent rate are proved.Numerical results indicate that the method is effective.