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Diophantine Approximations of Algebraic Irrationalities and Stability Theorems for Polynomial Decision Rules

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Computer Analysis of Images and Patterns (CAIP 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2124))

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Abstract

The theoretical aspects of the decision rules stability problem are considered in the article. The new metric theorems of the stability of the polynomial decision rules are proven. These theorems are sequent from the well-known results of approximating irrationalities by rational numbers obtained by Liouville, Roth and Khinchin. The problem of optimal correlation between deterministic and stochastic methods and quality criterion in pattern recognition problems is also discussed.

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References

  1. Lang, S.: Algebra. Reading, Mass. (1965)

    Google Scholar 

  2. Cassels, J.: An Introduction to Diophantine Approximation. Cambridge (1957)

    Google Scholar 

  3. Schmidt, W.: Diophantine Approximation. Springer (1980)

    Google Scholar 

  4. LeVeque, W.J.: Topics in Number Theory. Addison-Wesley, Reading, Mass. (1955)

    Google Scholar 

  5. Roth, K.F.: Rational Approximations to Algebraic Numbers. Mathematika, 2 (1955) 1–20

    Article  MathSciNet  Google Scholar 

  6. Khintchine, A.J.: Uber eine Klasse linearer Diophantische Approximationen. Rendiconti Circ. Mat. Palermo, 50 (1926) 170–195

    Article  Google Scholar 

  7. LeVeque, W.J.: On Maler’s U-numbers. J.Lond. Math. Soc., 28 220–229

    Google Scholar 

  8. Kargaev, P.P., Zhigljavsky, A.: Approximation of Real Numbers by Rationals: Some Metric Theorems. J. Number Theory, 65 (1996) 130–149

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Image processing Systems Institute of RAS, 151 Molodogvardejskaya St., IPSI RAS, 443001, Samara, Russia

    Vladimir M. Chernov

Authors
  1. Vladimir M. Chernov
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Editor information

Editors and Affiliations

  1. Faculty of Electronics and Information Technology Institute of Radioelectronics, Warsaw University of Technology, ul. Nowowiejska 15/19, 00-665, Warsaw, Poland

    Władysław Skarbek

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© 2001 Springer-Verlag Berlin Heidelberg

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Chernov, V.M. (2001). Diophantine Approximations of Algebraic Irrationalities and Stability Theorems for Polynomial Decision Rules. In: Skarbek, W. (eds) Computer Analysis of Images and Patterns. CAIP 2001. Lecture Notes in Computer Science, vol 2124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44692-3_22

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  • DOI: https://doi.org/10.1007/3-540-44692-3_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42513-7

  • Online ISBN: 978-3-540-44692-7

  • eBook Packages: Springer Book Archive

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