The Application of Homotopy Method In Solving Electrical Circuit Design Problem
This paper describes simple implementation of
homotopy (also called continuation) algorithm for determining the proper resistance of the resistor to dissipate energy at a specified rate of an electric circuit. Homotopy algorithm can be considered as a developing of the classical methods in numerical computing such as Newton-Raphson and fixed
point methods. In homoptopy methods, an embedding
parameter is used to control the convergence. The method purposed in this work utilizes a special homotopy called Newton homotopy. Numerical example solved in MATLAB is given to show the effectiveness of the purposed method
[1] R. E. Bank and D. J. Rose, (1981), "Global Approximate Newton Methods", Numer. Math., vol. 37, pp. 279-295.
[2] Ljiljana Trajkociv, (1998), "Homotopy Methods for Computing Diode
Circuit Operting Points", Wiley Reference Number 2526.
[3] W. Kuroki, K. Yamamura, and S. Furuki, (2007), "An Efficient Variable
Gain Homotopy Method Using the SPICE-Oriented Approach", IEEE
Transactions on Circuits and Systems-II: Express Briefs, VOL. 54, NO.7.
[4] K.Yamamura, H. Kubo and K. Horiuchi, "A Globally Convergent Algorithm Based on Fixed-Point Homotopy for the Solution of Nonlinear Resistive Circuits" Trans. IEICE, J70-A, 10, pp. 1430-
1438. 1987
[5] E Allgower And K. Georg, , (1994). "Numerical Path Following" Internet
Document, Colorado, U.S.A.
[6] C. B. Garcia and W. B Zangwill, (1981), "Pathways to Solutions, Fixed Points, and Equilibrium" Prentice Hall.
[7] M. Kojima, (1978), "On the Homotopic approach to systems of Equations
with separable Mappings" Math. Programming Study, 7, pp. 170-184.
[8] R. Saigal, (1983) "A homotopy for Solving Large, Sparse and Structured
Fixed Point Problems" Mathematics of Oerations Research, Vol. 8,
No. 4, U.S.A.
[9] J. M. Todd, (1978) "Exploiting Structur in Piecewise-Linear Homotopy
Algoritms for Solving Equations" School of Operation Research and
Industrial Engineering, College of Engineering, Cornell University,
Ithaca, NY, U.S.A.
[10] L. T. Watson, (1991), "A Survey of Probability-One Homotopy Methods
for Engineering Optimization" The Arabian Journal for Science and
Engioneering, Vol. 16, No. 28, pp. 297-323.
[11] L. T. Watson, D. E. Stewart, (1996), "Note on the End Game in Homotopy Zero Curve Tracking" ACM Transactions on
Mathematical Software, Vol. 22, No. 3, pp.281-187.
[12] L. T. Watson and A. P Morgan,., (1989), "Globally Convergent Homotopy Methods: A Tutorial" Elsevier Science Publishing Co.,
Inc., pp. 369-396, 655 Avenue of Americas, New Yorke.
[13] K. Yamamura., Kubo H. and Horiuchi, K., (1987) "A Globally Convergent Algorithm Based on Fixed-Point Homotopy for the
Solution of Nonlinear Resistive Circuits" Trans. IEICE, J70-A, 10,
pp. 1430-1438.
[14] K. Yamamura and K. Horiuchi, (1988), "Solving nonlinear resistive
networks by a homotopy method using a rectangular subdivision" Technical Report CS- 88-1, pp.1225-1228, Department of Computer
Science, Gunma University, Japan.
[15] S. C. Chapra and R. P. Canale, (2008), "Numerical Methods for Engineers" Fifth Edition, McGraw-Hall International Edition.
[16] K. Yamamura, K. Katou, and Ochiai, M., (1991), "Improving the Efficency of Integer Labeling Methods for Solving Systems of
Nonlinear Equations" IEICE Transactions, Vol. E 74, No. 6, pp.1463-1470.
[1] R. E. Bank and D. J. Rose, (1981), "Global Approximate Newton Methods", Numer. Math., vol. 37, pp. 279-295.
[2] Ljiljana Trajkociv, (1998), "Homotopy Methods for Computing Diode
Circuit Operting Points", Wiley Reference Number 2526.
[3] W. Kuroki, K. Yamamura, and S. Furuki, (2007), "An Efficient Variable
Gain Homotopy Method Using the SPICE-Oriented Approach", IEEE
Transactions on Circuits and Systems-II: Express Briefs, VOL. 54, NO.7.
[4] K.Yamamura, H. Kubo and K. Horiuchi, "A Globally Convergent Algorithm Based on Fixed-Point Homotopy for the Solution of Nonlinear Resistive Circuits" Trans. IEICE, J70-A, 10, pp. 1430-
1438. 1987
[5] E Allgower And K. Georg, , (1994). "Numerical Path Following" Internet
Document, Colorado, U.S.A.
[6] C. B. Garcia and W. B Zangwill, (1981), "Pathways to Solutions, Fixed Points, and Equilibrium" Prentice Hall.
[7] M. Kojima, (1978), "On the Homotopic approach to systems of Equations
with separable Mappings" Math. Programming Study, 7, pp. 170-184.
[8] R. Saigal, (1983) "A homotopy for Solving Large, Sparse and Structured
Fixed Point Problems" Mathematics of Oerations Research, Vol. 8,
No. 4, U.S.A.
[9] J. M. Todd, (1978) "Exploiting Structur in Piecewise-Linear Homotopy
Algoritms for Solving Equations" School of Operation Research and
Industrial Engineering, College of Engineering, Cornell University,
Ithaca, NY, U.S.A.
[10] L. T. Watson, (1991), "A Survey of Probability-One Homotopy Methods
for Engineering Optimization" The Arabian Journal for Science and
Engioneering, Vol. 16, No. 28, pp. 297-323.
[11] L. T. Watson, D. E. Stewart, (1996), "Note on the End Game in Homotopy Zero Curve Tracking" ACM Transactions on
Mathematical Software, Vol. 22, No. 3, pp.281-187.
[12] L. T. Watson and A. P Morgan,., (1989), "Globally Convergent Homotopy Methods: A Tutorial" Elsevier Science Publishing Co.,
Inc., pp. 369-396, 655 Avenue of Americas, New Yorke.
[13] K. Yamamura., Kubo H. and Horiuchi, K., (1987) "A Globally Convergent Algorithm Based on Fixed-Point Homotopy for the
Solution of Nonlinear Resistive Circuits" Trans. IEICE, J70-A, 10,
pp. 1430-1438.
[14] K. Yamamura and K. Horiuchi, (1988), "Solving nonlinear resistive
networks by a homotopy method using a rectangular subdivision" Technical Report CS- 88-1, pp.1225-1228, Department of Computer
Science, Gunma University, Japan.
[15] S. C. Chapra and R. P. Canale, (2008), "Numerical Methods for Engineers" Fifth Edition, McGraw-Hall International Edition.
[16] K. Yamamura, K. Katou, and Ochiai, M., (1991), "Improving the Efficency of Integer Labeling Methods for Solving Systems of
Nonlinear Equations" IEICE Transactions, Vol. E 74, No. 6, pp.1463-1470.
@article{"International Journal of Electrical, Electronic and Communication Sciences:49531", author = "Talib Hashim Hasan", title = "The Application of Homotopy Method In Solving Electrical Circuit Design Problem", abstract = "This paper describes simple implementation of
homotopy (also called continuation) algorithm for determining the proper resistance of the resistor to dissipate energy at a specified rate of an electric circuit. Homotopy algorithm can be considered as a developing of the classical methods in numerical computing such as Newton-Raphson and fixed
point methods. In homoptopy methods, an embedding
parameter is used to control the convergence. The method purposed in this work utilizes a special homotopy called Newton homotopy. Numerical example solved in MATLAB is given to show the effectiveness of the purposed method", keywords = "electrical circuit homotopy, methods, MATLAB, Newton homotopy", volume = "3", number = "1", pages = "1-3", }
