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

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• 作者：Rong Liu (1) (2)
  
  1. College of Computer and Information Science ; Fujian Agriculture and Forestry University ; Fuzhou ; 350002 ; China
  2. College of Mathematics and Computer Science ; Hunan Normal University ; Changsha ; 410081 ; China
  
• 关键词：uniqueness theorems ; power orthogonal polynomials ; Gaussian quadrature formula ; extended Chebyshev system ; Gaussian Birkhoff quadrature formula ; 42C05 ; 33C45
• 刊名：Acta Mathematicae Applicatae Sinica, English Series
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：31
• 期：1
• 页码：111-120
• 全文大小：223 KB
• 参考文献：1. Bojanov, BD (1978) Extremal problems in the set of polynomials with fixed multiplicities of zeros. Comp. Rend. Acad. Bulgare Sci. 31: pp. 377-400
  2. Bojanov, BD Oscillating polynomials of least L 1-norm. In: Hammerlin, G eds. (1982) Numerical Integration. Birkh盲user, Basel, pp. 25-33 CrossRef
  3. Bojanov, BD (1997) Gaussian quadrature formulas for Tchebycheff systems. East J. Approx 1: pp. 71-88
  4. Bojanov, BD, Braess, D, Dyn, N (1986) Generalized Gaussian quadrature formulas. J. Approx. Theory 46: pp. 335-353 CrossRef
  5. Lorentz, GG, Jetter, K, Riemenschneider, SD (1983) Birkhoff Interpolation. Addison Wesley Pub. Co., Reading, Massachusetts, London
  6. Micchelli, G, Rivlin, T (1973) Quadrature formulas and Hermite-Birkhoff interpolation. Adv. in Math. 11: pp. 93-111 CrossRef
  7. Nikolov, G (1989) Existence and uniqueness of Hermite-Birkhoff Gaussian quadrature formulas. Calcolo 26: pp. 41-59 CrossRef
  8. Shi, YG (1995) Generalized Gaussian quadrature formulas for Tchebycheff systems. Far East J. Appl. Math. 3: pp. 153-170
  9. Shi, YG (2003) Theory of Birkhoff Interpolation. Nova Science Publishers, Inc., New York
  10. Shi, YG (2006) Power Orthogonal Polynomials. Nova Science Publishers, Inc., New York
  11. Shi, YG, Xu, GL (2007) Construction of 蟽-orthogonal polynomials and Gaussian quadrature formulas. Adv. Comput. Math. 27: pp. 79-94 CrossRef
  
• 刊物主题：Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics;
• 出版者：Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
• ISSN：1618-3932

文摘

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.