j**u
发帖数: 6059 | 1 ☆─────────────────────────────────────☆
johnlee123 (no) 于 (Tue Jun 12 21:22:16 2007) 提到:
用牛顿迭代法求解非线性方程组，收敛非常慢，尽管最后能够收敛到预计的结果，但是
需要几百甚至上千步迭代。请问大虾这可能是什么原因引起的呢？多谢了！
按以往的经验，牛顿迭代收敛是很快的，只要初值合适，系数矩阵条件数不大，通常10
步以内就能收敛到合适的结果。如果系数矩阵条件数太大，那无论迭代多少步都无法收
敛，而不会像现在的情况这样迭代几百步之后收敛。
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longhei ($$$$$$$$$$$$) 于 (Tue Jun 12 21:44:49 2007) 提到:
who said Newton always converges in 10 steps (even with well-conditioned
coefficient matrix)?
10
☆────────────────────────────── | e***n
发帖数: 286 | 2 basically, it seems to me the newton method is among the fastest quality-
guaranteed algorithms. It is quadratic covergence. All other improvements
are at most superlinear convergence, such as various quasi-newton methods.
but newton methods are rarely used to solve practical problems, since it is
not descent-guaranteed and it consumes memory a lot. |
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