论文标题
M量敏感方程的不精确的牛顿方法
Inexact Newton Method for M-Tensor Equations
论文作者
论文摘要
我们首先研究了M量态方程的性能。特别是，我们表明，如果方程的恒定项是非负项，则可以通过找到较低维M量态方程的阳性解决方案来完成方程的非负解。然后，我们提出了一种不精确的牛顿方法，以找到对较低维方程的积极解决方案并确定其全局收敛性。我们还表明该方法的收敛速率是二次的。最后，我们进行数值实验来测试提出的牛顿方法。结果表明，提出的牛顿方法具有很好的数值性能。
We first investigate properties of M-tensor equations. In particular, we show that if the constant term of the equation is nonnegative, then finding a nonnegative solution of the equation can be done by finding a positive solution of a lower dimensional M-tensor equation. We then propose an inexact Newton method to find a positive solution to the lower dimensional equation and establish its global convergence. We also show that the convergence rate of the method is quadratic. At last, we do numerical experiments to test the proposed Newton method. The results show that the proposed Newton method has a very good numerical performance.
