论文标题
避免奇异性的多维根刺
Singularity-Avoiding Multi-Dimensional Root-Finder
论文作者
论文摘要
我们在本文中提出了一种新方法，我们将其命名为W4方法，以求解非线性方程系统。它可以被视为当该方法失败时要使用的Newton-Raphson〜（NR）方法的扩展。确实，我们的方法不仅可以应用于非单明一角的雅各布矩阵的普通问题，还可以应用于奇异雅各布人的问题，这实际上是所有使用雅各布矩阵反转的所有先前方法都无法解决。在本文中，我们证明（i）我们的新方案即使利用奇异价值分解也可以定义非单独的迭代图，（ii）在新迭代图中的一系列向量在某个条件下转移到正确的解决方案，（iii）在文学中，没有单个方法在远处提出的标准二维问题可以完全求解我们的求解。
We proposed in this paper a new method, which we named the W4 method, to solve nonlinear equation systems. It may be regarded as an extension of the Newton-Raphson~(NR) method to be used when the method fails. Indeed our method can be applied not only to ordinary problems with non-singular Jacobian matrices but also to problems with singular Jacobians, which essentially all previous methods that employ the inversion of the Jacobian matrix have failed to solve. In this article, we demonstrate that (i) our new scheme can define a non-singular iteration map even for those problems by utilizing the singular value decomposition, (ii) a series of vectors in the new iteration map converges to the right solution under a certain condition, (iii) the standard two-dimensional problems in the literature that no single method proposed so far has been able to solve completely are all solved by our new method.
