Skip to content
Research Article Open access CC BY 2.0

New Aspects of Double Bounded Polynomial Homotopy

H. Vazquez-Leal, A. Sarmiento-Reyes, Y. Khan, A. Yıldırım, U. Filobello-Nino, R. Castaneda-Sheissa, A.L. Herrera-May, V.M. Jimenez-Fernandez, S.F. Hernandez-Machuca, L. Cuellar-Hernandez

Journal of Advances in Mathematics and Computer Science · pp. 549–566 · Published 24 Jun 2013

10.9734/BJMCS/2013/2266

Abstract

This work presents some new aspects about the mathematical properties of the double bounded polynomial homotopy like: isolated symmetry branches equation and a study about initial and final points of the path and curvature radius. The application of the homotopy is illustrated by solving a mathematical problem and a nonlinear circuit.

Homotopy continuation methods multiple operating points

References (18)

  1. 1 587. Microelectronic circuits [DOI]
  2. 2 The modified nodal approach to network analysis [DOI]
  3. 3 Widely Convergent Method for Finding Multiple Solutions of Simultaneous Nonlinear Equations [DOI]
  4. 4 Artificial parameter homotopy methods for the DC operating point problem [DOI]
  5. 5 An efficient algorithm for finding multiple DC solutions based on the SPICE-oriented Newton homotopy method [DOI]
  6. 6 Multiparameter homotopy methods for finding DC operating points of nonlinear circuits [DOI]
  7. 7 A method for automatically finding multiple operating points in nonlinear circuits [DOI]
  8. 8 Delivering global DC convergence for large mixed-signal circuits via homotopy/continuation methods [DOI]
  9. 9 Numerical continuation scheme for tracing the double bounded hornotopy for analysing nonlinear circuits [DOI]
  10. 10 Homotopy method with a formal stop criterion applied to circuit simulation [DOI]
  11. 11 Double-Bounded Homotopy for Analysing Nonlinear Resistive Circuits [DOI]
  12. 12 Powering Multiparameter Homotopy-Based Simulation with a Fast Path-Following Technique [DOI]
  13. 13 Biparameter Homotopy-based Direct Current Simulation of Multistable Circuits [DOI]
  14. 14 A switching‐parameter algorithm for finding multiple solutions of nonlinear resistive circuits [DOI]
  15. 15 Tracing solution curves of non-linear equations with sharp turning points [DOI]
  16. 16 Constructive homotopy methods for finding all or multiple DC operating points of nonlinear circuits and systems [DOI]
  17. 17 An efficient continuation method for use in globally convergent dc circuit simulation [DOI]
  18. 18 Circuit Simulation Methods and Algorithms [DOI]

Cited by 11

Improved spherical continuation algorithm with application to the double-bounded homotopy (DBH)

D. Torres-Muñoz, H. Vazquez-Leal, L. Hernandez-Martinez · Computational and Applied Mathematics · 2013

Speed-up hyperspheres homotopic path tracking algorithm for PWL circuits simulations

A. Ramirez-Pinero, H. Vazquez-Leal, V. M. Jimenez-Fernandez · SpringerPlus · 2016

Modified Hyperspheres Algorithm to Trace Homotopy Curves of Nonlinear Circuits Composed by Piecewise Linear Modelled Devices

H. Vazquez-Leal, V. M. Jimenez-Fernandez, B. Benhammouda · The Scientific World Journal · 2014

Homotopy Path Planning for Terrestrial Robots Using Spherical Algorithm

Gerardo Diaz-Arango, Hector Vazquez-Leal, Luis Hernandez-Martinez · IEEE Transactions on Automation Science and Engineering · 2018

Homotopy-based direct current analysis with formal stop criterion

H. Vazquez-Leal, B. Benhammouda, K. Boubaker · 2014 IEEE 57th International Midwest Symposium on Circuits and Systems (MWSCAS) · 2014

Showing 5 of 11 known citations — external sources report more than can currently be individually listed.

Article metrics

Real usage data collected on this platform.

74

Page views

0

PDF downloads

34

Outbound clicks

11

Citations

Views over time

Views by country

Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".

Traffic sources

Referring site, by host.

Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.