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Journal of Zhejiang University SCIENCE A 2002 Vol.3 No.4 P.455-460

http://doi.org/10.1631/jzus.2002.0455


Gauss-Radau and Gauss-Lobatto formulae for the Jacobi weight and Gori-Micchelli weight functions


Author(s):  YANG Shi-jun

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310028, China

Corresponding email(s):   yangshijun@mail.hz.zj.cn

Key Words:  Quadrature, Gauss-Radau formula, Gauss-Lobatto formula, Gori-Micchelli weight


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YANG Shi-jun. Gauss-Radau and Gauss-Lobatto formulae for the Jacobi weight and Gori-Micchelli weight functions[J]. Journal of Zhejiang University Science A, 2002, 3(4): 455-460.

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T1 - Gauss-Radau and Gauss-Lobatto formulae for the Jacobi weight and Gori-Micchelli weight functions
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Abstract: 
The main purpose of this work is to find for any non-negative measure, the relations between the Gauss-Radau and gauss-Lobatto formula and Gauss formulae for the same measure. As applications, the author obtained the explicit Gauss-Radau and gauss-Lobatto formulae for the Jacobi weight and the gori-Micchelli weight.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Davis, P.J.,Rabinowitz, P. 1975, Methods of Numerical Integration, Academic Press, New York.

[2] Gautschi,W., 2000a, Gauss-Radau formulae for Jacobi and Laguerre weight functions. Math. and Comput.in Simulation, 54:403-412.

[3] Gautschi,W., 2000b, High-order Gauss-Lobatto formulae, Electr. Trans. Numer. Algorithms, 25: 213-222.

[4] Gori,L.,Miccheli,C.A.,1996. On weight functions which admit explicit Gauss-Turan quadrature formulas. Math. Computation, 65:1567-1581.

[5] Golub, G.H.,1973, Some modified matrix eigenvalue problems. SIAM Rev. 15: 318-334.

[6] Szegó,G.,1959. Orthogonal Polynomials, New York.

[7] Yang,S.J., Wang,X.H.,2002. Fourier-Chebyshev coefficients and Gauss-Turán quadrature with Chebyshev weight. Journal of Computational Mathematics (accepted).

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