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Properties of Padé approximants to stieltjes series and systems theory

Circuit Theory

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1105)

Abstract

The fact that Padé approximants of certain orders to a matrix Stieltjes series are realizable as open-circuit impedance matrices of RC-ideal transformer multiports is used to derive properties of such approximants. These properties include coefficient inequalities, the univalent nature of the approximants in a specified region of the complex plane and the coprimeness properties of the polynomial matrices in the matrix fraction description of the rational matrix approximants to a matrix Stieltjes series. Some known results will be shown to follow through network theory interpretations and new results concerning the rational approximants considered are derived.

Keywords

  • Ideal Transformer
  • Impedance Function
  • Polynomial Matrice
  • Matrix Case
  • Pade Approximants

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.

Research supported by National Science Foundation Grant 78-23141.

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References

  1. Basu, S. and Bose, N.K., "Matrix Stieltjes series and network models," SIAM J. Math. Anal., 14, no. 2 (1983), 209–222.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Newcomb, R.W., "Linear Multiport Synthesis," McGraw-Hill, New York, 1966.

    Google Scholar 

  3. Baker, G.A., "Essentials of Padé Approximants," Academic Press, New York, 1975.

    MATH  Google Scholar 

  4. Hazony, D., "Elements of Network Synthesis," Reinhold Publishing Corporation, New York, 1963.

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  5. Temes, C.G. and Lapatra, W., "Introduction to Circuit Synthesis and Design," McGraw-Hill, New York, 1977.

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  6. Talbot, A., "Some theorems on positive functions," IEEE Trans. Circuit Theory, 12, (1965), 607–608.

    CrossRef  MathSciNet  Google Scholar 

  7. Reza, F.M., "On the Schlicht behavior of certain impedance functions," IEEE Trans. Circuit Theory, 9, (1962), 231–232.

    CrossRef  Google Scholar 

  8. Bose, N.K., "Applied Multidimensional Systems Theory," Van Nostrand Reinhold Co., New York, 1982.

    MATH  Google Scholar 

  9. Kailath, T., "Linear Systems," Prentice-Hall, Englewood Cliffs, NJ, 1980.

    MATH  Google Scholar 

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© 1984 Springer-Verlag

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Bose, N.K. (1984). Properties of Padé approximants to stieltjes series and systems theory. In: Graves-Morris, P.R., Saff, E.B., Varga, R.S. (eds) Rational Approximation and Interpolation. Lecture Notes in Mathematics, vol 1105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072411

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  • DOI: https://doi.org/10.1007/BFb0072411

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13899-0

  • Online ISBN: 978-3-540-39113-5

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