一种基于病态问题的修正牛顿法

A Modified Newton Method Based on Ill-Conditioning Problem

针对初值在真解附近,由牛顿法得到的最终迭代结果远离真值的这一类病态问题,在对已有修正牛顿法进行研究的基础上,通过引入一个控制参数提出了一种新的修正牛顿法。进一步在完备的赋范线性空间中给出该修正牛顿法的收敛性证明与误差估计。最后,数值实验结果表明了这种新的修正牛顿法的有效性以及在收敛速度上的优越性。

A new modified newton method was presented by bringing a control parameter to solve the problem that the final iteration results was away from the true value for the initial value near the true solution based on the established modified newton method. Further the convergence proof of this modified algorithm and the error estimates in complete normed linear space were given. Finally,numerical experiments show that the modified algorithm is effective with the superiority of the convergence speed.