Advertisement

Time-Varying Inverse Square Root

  • Yunong ZhangEmail author
  • Dongsheng Guo
Chapter
  • 506 Downloads

Abstract

In this chapter, we propose, generalize, develop, and investigate different ZD models based on different ZFs for solving the time-varying inverse square root problem. In addition, this chapter shows modeling of the proposed ZD models using MATLAB Simulink techniques. The modeling results with different illustrative examples further substantiate the efficacy of such proposed ZD models for time-varying inverse square root finding.

Keywords

Inverse Square Root Problem Root Finding MATLAB Simulink Model Error-monitoring Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Seidel PM (1999) High-speed redundant reciprocal approximation. Integr VLSI J 28(1):1–12CrossRefMathSciNetGoogle Scholar
  2. 2.
    Blinn J (2003) Jim Blinn’s corner: notation, notation, notation. Elsevier, San FranciscoGoogle Scholar
  3. 3.
    Eberly D (2001) 3D game engine design. Elsevier, San FranciscoGoogle Scholar
  4. 4.
    Clenshaw CW, Olver FWJ (1986) Unrestricted algorithms for reciprocals and square roots. BIT Numer Math 26(4):475–492CrossRefMathSciNetGoogle Scholar
  5. 5.
    Lang T, Montuschi P (1999) Very high radix square root with prescaling and rounding and a combined division/square root unit. IEEE Trans Comput 48(8):827–841CrossRefMathSciNetGoogle Scholar
  6. 6.
    Pineiro JA, Bruguera JD (2002) High-speed double-precision computation of reciprocal, division, square root, and inverse square root. IEEE Trans Comput 51(12):1377–1388CrossRefMathSciNetGoogle Scholar
  7. 7.
    Ercegovac MD, Lang T, Muller JM, Tisserand A (2000) Reciprocation, square root, inverse square root, and some elementary functions using small multipliers. IEEE Trans Comput 49(7):628–637CrossRefMathSciNetGoogle Scholar
  8. 8.
    Mead C (1989) Analog VLSI and neural systems. Addison-Wesley Longman, BostonCrossRefzbMATHGoogle Scholar
  9. 9.
    Zhang Y, Yi C, Guo D, Zheng J (2011) Comparison on Zhang neural dynamics and gradient-based neural dynamics for online solution of nonlinear time-varying equation. Neural Comput Appl 20(1):1–7CrossRefGoogle Scholar
  10. 10.
    Zhang Y, Leithead WE, Leith DJ (2005) Time-series Gaussian process regression based on Toeplitz computation of \(O(N^2)\) operations and \(O(N)\)-level storage. In: Proceedings of the 44th IEEE international conference on decision and control, pp 3711–3716Google Scholar
  11. 11.
    Zhang Y, Li Z, Xie Y, Tan H, Chen P (2013) Z-type and G-type ZISR (Zhang inverse square root) solving. In: Proceedings of the 4th international conference on intelligent control and information processing, pp 123–128Google Scholar
  12. 12.
    Zhang Y, Li Z, Guo D, Li W, Chen P (2013) Z-type and G-type models for time-varying inverse square root (TVISR) solving. Soft Comput 17(11):2021–2032CrossRefGoogle Scholar
  13. 13.
    Zhang Y, Yu X, Xie Y, Tan H, Fan Z (2013) Solving for time-varying inverse square root by different ZD models based on different Zhang functions. In: Proceedings of the 25th Chinese control and decision conference, pp 1358–1363Google Scholar
  14. 14.
    Zhang Y, Guo X, Ma W (2008) Modeling and simulation of Zhang neural network for online time-varying equations solving based on MATLAB Simulink. In: Proceedings of the 7th international conference on machine learning and cybernetics, pp 805–810Google Scholar
  15. 15.
    Tan N, Chen K, Shi Y, Zhang Y (2009) Modeling, verification and comparison of Zhang neural net and gradient neural net for online solution of time-varying linear matrix equation. In: Proceedings of the 4th IEEE conference on industrial electronics and applications, pp 3698–3703Google Scholar
  16. 16.
    Ansari MS, Rahman SA (2011) DVCC-based non-linear feedback neural circuit for solving system of linear equations. Circuits Syst Signal Process 30(5):1029–1045CrossRefzbMATHGoogle Scholar
  17. 17.
    Zhang Y, Yi C (2011) Zhang neural networks and neural-dynamic method. Nova Science Publishers, New YorkGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of Information Science and TechnologySun Yat-sen UniversityGuangzhouChina

Personalised recommendations