Research on Efficient Numerical Analysis Method for Nonlinear Resistive Circuits and on the Properties of the Solutions of the above Circuits

非线性电阻电路高效数值分析方法及上述电路解的性质研究

• 批准号: 01550313
• 负责人: NISHI Tetsuo
• 金额: $ 1.15万
• 依托单位: Kyushu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1989
• 资助国家: 日本
• 起止时间: 1989 至 1990
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-01550313/
• 关键词: Nonlinear; Resistive circuits; Number of solutions; uniqueness of a solution; Efficient numerical analysis; Topological structure; 数値解法; 非線形回路; 回路トポロジ-; 一意解

We studied on the nonlinear resistive circuits composed of nonlinear resistive one-ports or nonlinear amplifiers and linear resistive elements including linear active elements. Fundamental problems concerning these circuits are, for example, efficient numerical analysis methods, existence and uniqueness of a solution, the number of solutions, and stability analysis of solutions. Many researchers have studied on these problems, but most problems have so far been unsolved completely. In this research we studied on efficient numerical method of piecewise-linear equations and the number of solutions of an important class of nonlinear equations.1. We proposed an efficient method to find all solutions of piecewise-linear equations. This method requires the amount of computation (multiplications) of O (Mn), where the capital letter O means the order of computational complexity, while previous best results so far known required the computatio of O (Mn^2) in the worst case. We presented the res … More ult at the 1989 ISCAS sponsored by IEEE CAS Society. We conjecture that our result is the best in the sense of computational complexity, but have not proven it yet.2. In the previous theoretical research on the nonlinear resistive circuits it has exclusively been assumed thatAssumption 1 : The v-i characteristics i=f (v) of nonlinear resistive one-ports and the amplification functions v_2=f (v_1) of nonlinear amplifiers are monotonically increasing.Under Assumption 1, however, we can obtain only the condition for the unique solution. To obtain more practical results we assume in this research that :Assumption 2 : The second derivative as well as the first derivative of the nonlinear function f (・) are always positive.Assumption 3 : Amplifiers have ideal saturation characteristics.Under these assumptions we investigated the number of solutions and gave some necessary and sufficient conditions concerning them. Some of them are the conditions for equations to have a finite number of solutions and the upper limit of the number of solutions. Less

本文研究了由非线性电阻性单端口或非线性放大器和线性电阻元件（包括线性有源元件）组成的非线性电阻性电路。关于这些电路的基本问题是，例如，有效的数值分析方法，解的存在性和唯一性，解的数量，以及解的稳定性分析。许多研究者对这些问题进行了研究，但大多数问题至今仍未得到彻底解决。本文研究了分段线性方程组的有效数值解法以及一类重要的非线性方程组的解的个数.提出了一种求分段线性方程组全部解的有效方法。这种方法需要O（Mn）的计算量（乘法），其中大写字母O表示计算复杂度的数量级，而迄今为止已知的以前最好的结果在最坏情况下需要O（Mn^2）的计算。我们提出了保留意见， ...更多信息 1989年由IEEE CAS Society主办的ISCAS。我们推测我们的结果在计算复杂度的意义上是最好的，但尚未证明.在以往对非线性电阻电路的理论研究中，只假定假设1：非线性电阻单端口的v-i特性i=f（v）和非线性放大器的放大函数v_2=f（v_1）是单调递增的，但在假设1下，我们只能得到唯一解的条件。为了得到更符合实际的结果，我们假定：假设2：非线性函数f（·）的二阶导数和一阶导数都是正的，假设3：放大器具有理想饱和特性，在这些假设下，我们研究了解的个数，并给出了它们的一些充要条件。其中一些是方程有有限个解的条件和解的个数的上限。少

项目成果

Tetsuo NISHI: "Circuit Theory in Japan" IEEE Transactions on Education. vol. 32, no. 3. 355-358 (1989)

Tetsuo NISHI：“日本的电路理论”IEEE 教育学报。

Tetsuo NISHI: "An efficient method to find all solutions of piecewise-linear resistive circuits" Proc. of 1989 IEEE International Symposium on Circuits and Systems. vol. 3. 2052-2055 (1989)

Tetsuo NISHI：“一种寻找分段线性电阻电路所有解的有效方法”Proc。

Tetsuo NISHI: "Circuit Theory in Japan" IEEE Transactions on Education. 32. 355-358 (1989)

Tetsuo NISHI：“日本的电路理论”IEEE 教育学报。

西 哲生 川根 祐二: "非線形抵抗回路の解の個数に関する一考察" 電子情報通信学会 技術研究報告. CAS89ー96. 31-36 (1989)

Tetsuo Nishi 和 Yuji Kawane：“非线性电阻电路解数的研究”IEICE CAS89-96 (1989)。

Tetsuo NISHI Hisashi INOUE: "On the Relation between the learning Rate and the Distance of Patterns in the Classification by Neural Network" Proc.of 1990 JOINT TECHNICAL CONFERENCE ON CIRCUITS/SYSTEMS,COMPUTERS AND COMMUNICATIONS. 375-380 (1990)

Tetsuo NISHI Hisashi INOUE：“On the Relation Between the Learning Rate and the Distance of Patterns in the Classification by Neural Network”Proc.of 1990 电路/系统、计算机和通信联合技术会议。