论文标题
适应了时变和静态矩阵问题的AZNN方法
Adapted AZNN Methods for Time-Varying and Static Matrix Problems
论文作者
论文摘要
我们提出了适应的张神经网络（AZNN），其中指数衰减常数$η$的参数设置和基本Znn的启动阶段的长度适用于当前的问题。具体而言，我们使用AZNN研究实验，以时变平方矩阵因子化，作为时变的对称矩阵的产物以及随时间变化的矩阵平方根问题。与Znn中通常使用的小$η$值和最小的启动长度阶段不同，我们适应了基本的ZNN方法，可以使用Euler的低精度有限差异公式使用大型甚至巨大的$η$设置和任意长度启动。这些适应性提高了AZNN收敛的速度，并降低了我们所选问题的解决方案误差界限，从而显着到接近机器常数甚至较低的水平。 参数变化的AZNN还使我们能够可靠地找到静态矩阵的完整等级对称器，例如，对于Kahan和Frank矩阵，以及具有高度不良的特征值和复杂的Jordan dimensions的矩阵，从$ n = 2 $上开始。在以前从未成功计算出全等级静态矩阵对称器的情况下，这有助于。
We present adapted Zhang Neural Networks (AZNN) in which the parameter settings for the exponential decay constant $η$ and the length of the start-up phase of basic ZNN are adapted to the problem at hand. Specifically we study experiments with AZNN for time-varying square matrix factorizations as a product of time-varying symmetric matrices and for the time-varying matrix square roots problem. Differing from generally used small $η$ values and minimal start-up length phases in ZNN, we adapt the basic ZNN method to work with large or even gigantic $η$ settings and arbitrary length start-ups using Euler's low accuracy finite difference formula. These adaptations improve the speed of AZNN's convergence and lower its solution error bounds for our chosen problems significantly to near machine constant or even lower levels. Parameter-varying AZNN also allows us to find full rank symmetrizers of static matrices reliably, for example for the Kahan and Frank matrices and for matrices with highly ill-conditioned eigenvalues and complicated Jordan structures of dimensions from $n = 2$ on up. This helps in cases where full rank static matrix symmetrizers have never been successfully computed before.
