一种广义多变量牛顿法
A Generalized Multivariable Newton Method
摘要：
众所周知，当初始猜测不属于特定的平方收敛区域时，牛顿法可能不收敛。我们提出了一个家庭的新的变种的牛顿方法具有潜在的优势，有一个更大的收敛区域，以及更理想的性能附近的解决方案。我们证明了新的家庭的平方收敛，并提供了具体的界限的渐近误差常数。我们通过测试问题，包括两个和六个变量多项式系统，以及一个具有挑战性的信号处理的例子说明了新方法的优点。我们提出了一个数值实验方法，它使用了大量的随机初始猜测的一些方法，从新的家庭，反过来提供建议，采用的方法是最好使用在一个特定的搜索域。
英文摘要：
It is well known that the Newton method may not converge when the initial guess does not belong to a specific quadratic convergence region. We propose a family of new variants of the Newton method with the potential advantage of having a larger convergence region as well as more desirable properties near a solution. We prove quadratic convergence of the new family, and provide specific bounds for the asymptotic error constant. We illustrate the advantages of the new methods by means of test problems, including two and six variable polynomial systems, as well as a challenging signal processing example. We present a numerical experimental methodology which uses a large number of randomized initial guesses for a number of methods from the new family, in turn providing advice as to which of the methods employed is preferable to use in a particular search domain.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
