IEICE TRANSACTIONS on transactions
Solving Nonlinear Resistive Networks by a Homotopy Method Using a Rectangular Subdivision
Summary :
This paper presents an efficient algorithm for solving bipolar transistor networks. In our algorithm, the network equation f (x)=0 is solved by a homotopy method, in which a homotopy h (x, t)=f (x)-(1-t) f (x0) is introduced and the solution curve of h (x, t)=0 is traced from an obvious solution (x0, 0) to the solution (x*, 1) which we seek. It is shown that the convergence of the algorithm is guaranteed by fairly mild conditions. A rectangular subdivision and an upper bounding technique of linear programming are used for tracing the solution curve. Our rectangular algorithm is much more efficient than the conventional simplicial type algorithms. Some numerical examples are given in order to demonstrate the effectiveness of the algorithm. The advantages of the rectangular algorithm are as follows. (1) Convergence is guaranteed by fairly general conditions. (2) There is no need to evaluate Jacobian matrices. (3) There is no need to invert matrices except for the first step; only pivoting operations are necessary. (4) The replacement rule of vertices is very simple. (5) The computational complexity is markedly reduced compared with the simplicial algorithm. (6) The computational efficiency can be greatly improved by choosing the grid sizes of the rectangular subdivision pertinently according to the nonlinearity of the equation.
- Publication
- IEICE TRANSACTIONS on transactions Vol.E72-E No.5 pp.584-594
- Publication Date
- 1989/05/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Circuit Theory
Authors
Keyword
Latest Issue
Copyrights notice of machine-translated contents
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Cite this
Copy
Kiyotaka YAMAMURA, Kazuo HORIUCHI, "Solving Nonlinear Resistive Networks by a Homotopy Method Using a Rectangular Subdivision" in IEICE TRANSACTIONS on transactions,
vol. E72-E, no. 5, pp. 584-594, May 1989, doi: .
Abstract: This paper presents an efficient algorithm for solving bipolar transistor networks. In our algorithm, the network equation f (x)=0 is solved by a homotopy method, in which a homotopy h (x, t)=f (x)-(1-t) f (x0) is introduced and the solution curve of h (x, t)=0 is traced from an obvious solution (x0, 0) to the solution (x*, 1) which we seek. It is shown that the convergence of the algorithm is guaranteed by fairly mild conditions. A rectangular subdivision and an upper bounding technique of linear programming are used for tracing the solution curve. Our rectangular algorithm is much more efficient than the conventional simplicial type algorithms. Some numerical examples are given in order to demonstrate the effectiveness of the algorithm. The advantages of the rectangular algorithm are as follows. (1) Convergence is guaranteed by fairly general conditions. (2) There is no need to evaluate Jacobian matrices. (3) There is no need to invert matrices except for the first step; only pivoting operations are necessary. (4) The replacement rule of vertices is very simple. (5) The computational complexity is markedly reduced compared with the simplicial algorithm. (6) The computational efficiency can be greatly improved by choosing the grid sizes of the rectangular subdivision pertinently according to the nonlinearity of the equation.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e72-e_5_584/_p
Copy
@ARTICLE{e72-e_5_584,
author={Kiyotaka YAMAMURA, Kazuo HORIUCHI, },
journal={IEICE TRANSACTIONS on transactions},
title={Solving Nonlinear Resistive Networks by a Homotopy Method Using a Rectangular Subdivision},
year={1989},
volume={E72-E},
number={5},
pages={584-594},
abstract={This paper presents an efficient algorithm for solving bipolar transistor networks. In our algorithm, the network equation f (x)=0 is solved by a homotopy method, in which a homotopy h (x, t)=f (x)-(1-t) f (x0) is introduced and the solution curve of h (x, t)=0 is traced from an obvious solution (x0, 0) to the solution (x*, 1) which we seek. It is shown that the convergence of the algorithm is guaranteed by fairly mild conditions. A rectangular subdivision and an upper bounding technique of linear programming are used for tracing the solution curve. Our rectangular algorithm is much more efficient than the conventional simplicial type algorithms. Some numerical examples are given in order to demonstrate the effectiveness of the algorithm. The advantages of the rectangular algorithm are as follows. (1) Convergence is guaranteed by fairly general conditions. (2) There is no need to evaluate Jacobian matrices. (3) There is no need to invert matrices except for the first step; only pivoting operations are necessary. (4) The replacement rule of vertices is very simple. (5) The computational complexity is markedly reduced compared with the simplicial algorithm. (6) The computational efficiency can be greatly improved by choosing the grid sizes of the rectangular subdivision pertinently according to the nonlinearity of the equation.},
keywords={},
doi={},
ISSN={},
month={May},}
Copy
TY - JOUR
TI - Solving Nonlinear Resistive Networks by a Homotopy Method Using a Rectangular Subdivision
T2 - IEICE TRANSACTIONS on transactions
SP - 584
EP - 594
AU - Kiyotaka YAMAMURA
AU - Kazuo HORIUCHI
PY - 1989
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E72-E
IS - 5
JA - IEICE TRANSACTIONS on transactions
Y1 - May 1989
AB - This paper presents an efficient algorithm for solving bipolar transistor networks. In our algorithm, the network equation f (x)=0 is solved by a homotopy method, in which a homotopy h (x, t)=f (x)-(1-t) f (x0) is introduced and the solution curve of h (x, t)=0 is traced from an obvious solution (x0, 0) to the solution (x*, 1) which we seek. It is shown that the convergence of the algorithm is guaranteed by fairly mild conditions. A rectangular subdivision and an upper bounding technique of linear programming are used for tracing the solution curve. Our rectangular algorithm is much more efficient than the conventional simplicial type algorithms. Some numerical examples are given in order to demonstrate the effectiveness of the algorithm. The advantages of the rectangular algorithm are as follows. (1) Convergence is guaranteed by fairly general conditions. (2) There is no need to evaluate Jacobian matrices. (3) There is no need to invert matrices except for the first step; only pivoting operations are necessary. (4) The replacement rule of vertices is very simple. (5) The computational complexity is markedly reduced compared with the simplicial algorithm. (6) The computational efficiency can be greatly improved by choosing the grid sizes of the rectangular subdivision pertinently according to the nonlinearity of the equation.
ER -
English
