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Time-Varying Square Root

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Zhang Functions and Various Models
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Abstract

In this chapter, focusing on time-varying square root finding, we propose, generalize, develop, and investigate different ZFs as the error-monitoring functions, which lead to different ZD models. Then, toward the final purpose of field programmable gate array (FPGA) and application-specific integrated circuit (ASIC) realization, the MATLAB Simulink modeling and verification of such different ZD models are shown. Both theoretical analysis and modeling results further substantiate the efficacy of the proposed ZD models for time-varying square root finding.

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References

  1. IEEE (1985) IEEE standard for binary floating-point arithmetic. IEEE standard 754. IEEE Computer Society

    Google Scholar 

  2. Mathews JH, Fink KD (2005) Numerical methods using MATLAB. Publishing House of Electronics Industry, Beijing

    Google Scholar 

  3. Lin C (2005) Numerical computation methods. Science Press, Beijing

    Google Scholar 

  4. Majerski S (1985) Square-rooting algorithms for high-speed digital circuits. IEEE Trans Comput C-34(8):724–733

    Google Scholar 

  5. Takahashi D (2000) Implementation of multiple-precision parallel division and square root on distributed-memory parallel computers. In: Proceedings of international workshops on parallel processing, pp 229–235

    Google Scholar 

  6. Kong F, Cai Z, Yu J, Li DX (2006) Improved generalized Atkin algorithm for computing square roots in finite fields. Inf Process Lett 98(1):1–5

    Article  MATH  MathSciNet  Google Scholar 

  7. Pineiro JA, Bruguera JD (2002) High-speed double-precision computation of reciprocal, division, square root, and inverse square root. IEEE Trans Comput 51(12):1377–1388

    Article  MathSciNet  Google Scholar 

  8. 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):628–637

    Article  MathSciNet  Google Scholar 

  9. Zhang YN, 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 3711–3716

    Google Scholar 

  10. Mead C (1989) Analog VLSI and neural systems. Addison-Wesley Longman, Boston

    Book  MATH  Google Scholar 

  11. Zhang Y, Ma W, Li K, Yi C (2008) Brief history and prospect of coprocessors. China Acad J Electron Publ House 13:115–117

    Google Scholar 

  12. Zhang Y, Ke Z, Xu P, Yi C (2010) Time-varying square roots finding via Zhang dynamics versus gradient dynamics and the former’s link and new explanation to Newton-Raphson iteration. Inf Process Lett 110(24):1103–1109

    Article  MathSciNet  Google Scholar 

  13. Zhang Y, Yin Y, Guo D, Li W, Ke Z (2013) Different Zhang functions leading to different ZD models illustrated via time-varying square roots finding. In: Proceedings of the 4th international conference on intelligent control and information processing, pp 277–282

    Google Scholar 

  14. 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):1–7

    Article  Google Scholar 

  15. Zhang Y, Yi C (2011) Zhang neural networks and neural-dynamic method. Nova Science Publishers, New York

    Google Scholar 

  16. Bushard LB (1983) A minimum table size result for higher radix nonrestoring division. IEEE Trans Comput C-32(6):521–526

    Google Scholar 

  17. Trivedi K, Ercegovac M (1977) On-line algorithms for division and multiplication. IEEE Trans Comput C-26(7):681–687

    Google Scholar 

  18. Ansari MS, Rahman SA (2011) DVCC-based non-linear feedback neural circuit for solving system of linear equations. Circuits, Syst Signal Process 30(5):1029–1045

    Article  MATH  Google Scholar 

  19. Shanblatt MA (2005) A Simulink-to-FPGA implementation tool for enhanced design flow. In: Proceedings of the IEEE international conference on microelectronic systems education, pp 89–90

    Google Scholar 

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Correspondence to Yunong Zhang .

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Zhang, Y., Guo, D. (2015). Time-Varying Square Root. In: Zhang Functions and Various Models. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47334-4_3

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  • DOI: https://doi.org/10.1007/978-3-662-47334-4_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-47333-7

  • Online ISBN: 978-3-662-47334-4

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