A globally and quadratically convergent algorithm for solving nonlinear resistive networks
A globally and quadratically convergent algorithm for solving nonlinear resistive networks
复制标题
求解非线性电阻网络的全局二次收敛算法
DOI：
10.1109/43.55173
复制
发表时间：
1990
期刊：
影响因子：
--
通讯作者：
K. Horiuchi
中科院分区：
文献类型：
--
作者：
K. Yamamura;K. Horiuchi
本文提出了一种求解双极晶体管网络的全局收敛算法，该算法也是二次收敛的。该算法是基于同伦方法使用矩形细分。由于该算法使用矩形，它是更有效的比传统的单纯型算法。对一般的非线性电阻网络，证明了该算法的全局收敛性。这里，术语全局收敛意味着可以容易地获得导致解的起始点。提出了一种有效的加速技术，提高了矩形算法的局部收敛速度。通过这种技术，由算法产生的近似解序列二次收敛到精确解。此外，在这种情况下，每次迭代所涉及的计算工作几乎与牛顿法相同。因此，当算法足够接近解时，它变得与牛顿法一样有效。研究还表明，可以将稀疏矩阵技术引入矩形算法，并利用方程组的部分线性性来提高计算效率。最后给出了数值算例，验证了算法的有效性. >
A globally convergent algorithm that is also quadratically convergent for solving bipolar transistor networks is proposed. The algorithm is based on the homotopy method using a rectangular subdivision. Since the algorithm uses rectangles, it is much more efficient than the conventional simplicial-type algorithms. It is shown that the algorithm is globally convergent for a general class of nonlinear resistive networks. Here, the term globally convergent means that a starting point which leads to the solution can be obtained easily. An efficient acceleration technique which improves the local convergence speed of the rectangular algorithm is proposed. By this technique, the sequence of the approximate solutions generated by the algorithm converges to the exact solution quadratically. Also, in this case the computational work involved in each iteration is almost identical to that of Newton's method. Therefore, the algorithm becomes as efficient as Newton's method when it arrives sufficiently close to the solution. It is also shown that sparse-matrix techniques can be introduced to the rectangular algorithm, and the partial linearity of the system of equations can be exploited to improve the computational efficiency. Some numerical examples are also given in order to demonstrate the effectiveness of the proposed algorithm. >