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A uniqueness theorem of a system of nonlinear equations and its applications

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Abstract

A uniqueness theorem of a solution of a system of nonlinear equations is given. Using this result uniqueness theorems for power orthogonal polynomials, for a Gaussian quadrature formula of an extended Chebyshev system, and for a Gaussian Birkhoff quadrature formula are easily deduced.

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References

  1. Bojanov, B.D. Extremal problems in the set of polynomials with fixed multiplicities of zeros. Comp. Rend. Acad. Bulgare Sci., 31: 377–400 (1978)

    Google Scholar 

  2. Bojanov, B.D. Oscillating polynomials of least L 1-norm. In: Numerical Integration (G. Hammerlin, Ed.), p.25–33, ISNM 57, Birkhäuser, Basel, 1982

    Chapter  Google Scholar 

  3. Bojanov, B.D. Gaussian quadrature formulas for Tchebycheff systems. East J. Approx, 1: 71–88 (1997)

    MathSciNet  Google Scholar 

  4. Bojanov, B.D., Braess, D., Dyn, N. Generalized Gaussian quadrature formulas. J. Approx. Theory, 46: 335–353 (1986)

    Article  MathSciNet  Google Scholar 

  5. Lorentz, G.G., Jetter, K., Riemenschneider, S.D. Birkhoff Interpolation. Addison Wesley Pub. Co., Reading, Massachusetts, London, 1983

    MATH  Google Scholar 

  6. Micchelli, G., Rivlin, T. Quadrature formulas and Hermite-Birkhoff interpolation. Adv. in Math., 11: 93–111 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  7. Nikolov, G. Existence and uniqueness of Hermite-Birkhoff Gaussian quadrature formulas. Calcolo, 26: 41–59 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  8. Shi, Y.G. Generalized Gaussian quadrature formulas for Tchebycheff systems. Far East J. Appl. Math., 3: 153–170 (1995)

    Google Scholar 

  9. Shi, Y.G. Theory of Birkhoff Interpolation. Nova Science Publishers, Inc., New York, 2003

    MATH  Google Scholar 

  10. Shi, Y.G. Power Orthogonal Polynomials. Nova Science Publishers, Inc., New York, 2006

    MATH  Google Scholar 

  11. Shi, Y.G., Xu, G.L. Construction of σ-orthogonal polynomials and Gaussian quadrature formulas. Adv. Comput. Math., 27: 79–94 (2007)

    Article  MATH  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. College of Computer and Information Science, Fujian Agriculture and Forestry University, Fuzhou, 350002, China

    Rong Liu

  2. College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081, China

    Rong Liu

Authors
  1. Rong Liu
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Correspondence to Rong Liu.

Additional information

Supported by the National Natural Science Foundation of China (No. 11171100, 10871065 and 11071064), and by the Research Project of Fujian Agriculture and Forestry University (No. KXML2028A).

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Liu, R. A uniqueness theorem of a system of nonlinear equations and its applications. Acta Math. Appl. Sin. Engl. Ser. 31, 111–120 (2015). https://doi.org/10.1007/s10255-015-0454-8

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  • DOI: https://doi.org/10.1007/s10255-015-0454-8

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