**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30169

##### The Application of Homotopy Method In Solving Electrical Circuit Design Problem

**Authors:**
Talib Hashim Hasan

**Abstract:**

**Keywords:**
electrical circuit homotopy,
methods,
MATLAB,
Newton homotopy

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1328344

**References:**

[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.