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δ函数Legendre非线性逼近的收敛性 被引量：3

Convergence of the Legendre nonlinear approximations to the Dirac function
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摘要 讨论了利用Legendre多项式母函数的非线性逼近,证明了当这类非线性逼近应用于Diracδ函数时逼近是收敛的,且导出了逼近误差. The nonlinear approximations based on the generating functions of the Legendre polynomials were studied. It was proved that such nonlinear approximations to the Dirac delta function on [-1,1] were convergent. Moreover, the approximate errors was examined.
作者 潘云兰
机构地区 浙江师范大学数理学院
出处 《浙江师范大学学报（自然科学版）》 CAS 2005年第4期367-371,共5页 Journal of Zhejiang Normal University:Natural Sciences
基金 浙江省留学回国基金会留学回国人员科研启动基金 浙江师范大学数学重点专业基金
关键词 非线性逼近 母函数方法 Diracδ函数 LEGENDRE多项式 nonlinear approximation generating function method Dirac delta function Legendre polynomial
分类号 O241.5 [理学—计算数学]
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参考文献10

  • 1Brezinski C. Padé-Type Approximation and General Orthogonal Polynomials,ISNM 50[M]. Basel:Birkhaeuser Verlag,1980.
  • 2Charron R J ,Small R D. On weighting schemes associated with the generating function method[A]. Chui C K,Schumaker L L,Ward J D. Approximation Theory VI(Vol. 1 )[C]. New York: Academic Press Inc, 1989 : 133- 136.
  • 3Chisholm J S R,Common A K. Generalizations of Padé approximation for Chebyshev series[A]. Butzer P L,Fehér F,Christoffel E B.The Influence of His Work on Mathematics and the Physical Sciences[C]. Basel:Birkhaeuser Verlag, 1979.
  • 4Garibotti C R,Grinstein F F. A summation procedure for expansions in orthogonal polynomials[J]. Rev Brasileira Fis,1977, 7(3):557-567.
  • 5Small R D. The generating function method of nonlinear approximation[J]. SIAM J Num Anal,1988,25(1) :235-244.
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  • 8Parker G A ,Zhu W, Huang Y H, et al. Matrix pseudo-spectroscopy:iterative calculation of matrix eigenvalues and eigenvectors of large matrices using a polynomial expansion of the Dirac delta function[J]. Comput Phys Commun, 1996,96(1 ):27-35.
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同被引文献14

  • 1潘云兰.δ函数的导函数的Legendre非线性逼近[J].浙江师范大学学报（自然科学版）,2006,29(4):373-377. 被引量：1
  • 2潘云兰,杨文善.符号函数的Legendre非线性逼近[J].高等学校计算数学学报,2007,29(2):166-175. 被引量：1
  • 3Brezinski C.Padé-Type Approximation and General Orthogonal Polynomials,ISNM 50[M].Basel:Birkh(a)user Verlag,1980.
  • 4Charron R J,Small R D.On weighting schemes associated with the generating function method[C]//Chui C K,Schumaker L L,Ward J D.Approximation Theory Ⅵ:Vol.1.New York:Academic Press Inc,1989:133-136.
  • 5Chisholm J S R,Common A K.Generalizations of Padé approximation for Chebyshev series[C]//Butzer P L,Fehér F,Christoffel E B.The Influence of His Work on Mathematics and the Physical Sciences.Basel:Birkh(a)user Verlag,1979.
  • 6Garibotti C R,Grinstein F F.A summation procedure for expansions in orthogonal polynomials[J].Rev Brasileira Fis,1977,7 (3):557-567.
  • 7Small R D.The generating function method of nonlinear approximation[J].SIAM J Num Anal,1988,25(1):235-244.
  • 8Hildebrand F B.Introduction to Numerical Analysis[M].New York:Dover Publications Inc,1987.
  • 9曹志远,邹贵平,唐寿高.时变动力学的Legendre级数解[J].固体力学学报,2000,21(2):102-108. 被引量：8
  • 10范庆忠,王雨苗.用勒让德多项式逼近结构的瞬态响应[J].河海大学学报（自然科学版）,2002,30(2):26-29. 被引量：1

引证文献3

二级引证文献1

浙江师范大学学报（自然科学版）
2005年 第4期

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