Path Following Circuits--SPICE-Oriented Numerical Methods Where Formulas are Described by Circuits--
Summary :
Path following circuits (PFC's) are circuits for solving nonlinear problems on the circuit simulator SPICE. In the method of PFC's, formulas of numerical methods are described by circuits, which are solved by SPICE. Using PFC's, numerical analysis without programming is possible, and various techniques implemented in SPICE will make the numerical analysis very efficient. In this paper, we apply the PFC's of the homotopy method to various nonlinear problems (excluding circuit analysis) where the homotopy method is proven to be globally convergent; namely, we apply the method to fixed-point problems, linear programming problems, and nonlinear programming problems. This approach may give a new possibility to the fields of applied mathematics and operations research. Moreover, this approach makes SPICE applicable to a broader class of scientific problems.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E88-A No.4 pp.825-831
- Publication Date
- 2005/04/01
- Publicized
- Online ISSN
- DOI
- 10.1093/ietfec/e88-a.4.825
- Type of Manuscript
- Special Section PAPER (Special Section on Selected Papers from the 17th Workshop on Circuits and Systems in Karuizawa)
- Category
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Kiyotaka YAMAMURA, Wataru KUROKI, Hideaki OKUMA, Yasuaki INOUE, "Path Following Circuits--SPICE-Oriented Numerical Methods Where Formulas are Described by Circuits--" in IEICE TRANSACTIONS on Fundamentals,
vol. E88-A, no. 4, pp. 825-831, April 2005, doi: 10.1093/ietfec/e88-a.4.825.
Abstract: Path following circuits (PFC's) are circuits for solving nonlinear problems on the circuit simulator SPICE. In the method of PFC's, formulas of numerical methods are described by circuits, which are solved by SPICE. Using PFC's, numerical analysis without programming is possible, and various techniques implemented in SPICE will make the numerical analysis very efficient. In this paper, we apply the PFC's of the homotopy method to various nonlinear problems (excluding circuit analysis) where the homotopy method is proven to be globally convergent; namely, we apply the method to fixed-point problems, linear programming problems, and nonlinear programming problems. This approach may give a new possibility to the fields of applied mathematics and operations research. Moreover, this approach makes SPICE applicable to a broader class of scientific problems.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e88-a.4.825/_p
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@ARTICLE{e88-a_4_825,
author={Kiyotaka YAMAMURA, Wataru KUROKI, Hideaki OKUMA, Yasuaki INOUE, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Path Following Circuits--SPICE-Oriented Numerical Methods Where Formulas are Described by Circuits--},
year={2005},
volume={E88-A},
number={4},
pages={825-831},
abstract={Path following circuits (PFC's) are circuits for solving nonlinear problems on the circuit simulator SPICE. In the method of PFC's, formulas of numerical methods are described by circuits, which are solved by SPICE. Using PFC's, numerical analysis without programming is possible, and various techniques implemented in SPICE will make the numerical analysis very efficient. In this paper, we apply the PFC's of the homotopy method to various nonlinear problems (excluding circuit analysis) where the homotopy method is proven to be globally convergent; namely, we apply the method to fixed-point problems, linear programming problems, and nonlinear programming problems. This approach may give a new possibility to the fields of applied mathematics and operations research. Moreover, this approach makes SPICE applicable to a broader class of scientific problems.},
keywords={},
doi={10.1093/ietfec/e88-a.4.825},
ISSN={},
month={April},}
Copy
TY - JOUR
TI - Path Following Circuits--SPICE-Oriented Numerical Methods Where Formulas are Described by Circuits--
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 825
EP - 831
AU - Kiyotaka YAMAMURA
AU - Wataru KUROKI
AU - Hideaki OKUMA
AU - Yasuaki INOUE
PY - 2005
DO - 10.1093/ietfec/e88-a.4.825
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E88-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 2005
AB - Path following circuits (PFC's) are circuits for solving nonlinear problems on the circuit simulator SPICE. In the method of PFC's, formulas of numerical methods are described by circuits, which are solved by SPICE. Using PFC's, numerical analysis without programming is possible, and various techniques implemented in SPICE will make the numerical analysis very efficient. In this paper, we apply the PFC's of the homotopy method to various nonlinear problems (excluding circuit analysis) where the homotopy method is proven to be globally convergent; namely, we apply the method to fixed-point problems, linear programming problems, and nonlinear programming problems. This approach may give a new possibility to the fields of applied mathematics and operations research. Moreover, this approach makes SPICE applicable to a broader class of scientific problems.
ER -
English
