CAJ | 학술논문

研究了在实Hilbert空间中，求解非线性不适定问题的方法。通过对修正的三阶牛顿法进行Tikhonov正则化，得到新的迭代格式。在适当的条件下选取正则化参数，应用广义偏差准则，得出该迭代格式是单调的且是收敛性的。结果表明此迭代格式可应用于求解非线性不适定问题。
연구료재실Hilbert공간중，구해비선성불괄정문제적방법。통과대수정적삼계우돈법진행Tikhonov정칙화，득도신적질대격식。재괄당적조건하선취정칙화삼수，응용엄의편차준칙，득출해질대격식시단조적차시수렴성적。결과표명차질대격식가응용우구해비선성불괄정문제。
A method for solving nonlinear ill-posed problems in real Hilbert space was mainly studied . Through Tikhonov regularizing the modified Newton method ,an iterative form was obtained .The regu-larization parameter was chose under suitable conditions ,and the generalized error criterion was used ,so that the iterative scheme is monotone and convergence .From the result it could be seen that the nonlin-ear ill-posed problems can be solved by using the iterative scheme .