规范化Katzenelson算法解曲线的研讨

Discussion on the Solution Curve of Canonical Katzenelson Algorithm

规范化Katzenelson算法是L.O.Chua在文献[1]中提出的,它是规范化分段线性化电阻网络著名的迭代算法。它需选Jacobain矩阵行列式大于零的区域的内点为初始值.迭代过程形成的解曲线,从初始值开始经过若干个区域终止于某个解点.本文推导出解曲线从一个区域进入邻域的完整的判别式,可选任何区域的内点为初始值,解曲线到达某个解点后可以继续前进,以寻找其它的解,故也适合于多解网络的求解。

Canonical Katzenelson algorithm is presented by L.O.Chua in the references[1]. It's a well known algorithm for solving pieeewise-lincar resistive networks.In the iterative process,the solution curve from the starting point(x^(0) converges to a solution,but the starting point must be in the area where Jacobian matrix satisfies det J>0. In this paper,we present the criterion for solution curve from one area to another.We can select the starting point in any area also.When one solution is got,we can go on to get another solution.So it is easy to gain all solution in the multi-solution networks.