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Jacobi and Laguerre quasi-orthogonal approximations and related interpolations

Authors: Guo Ben-yu, Sun Tao and Zhang Chao
Journal: Math. Comp. 82 (2013), 413-441
MSC (2010): Primary 41A10, 41A05, 41A30, 65L60
Published electronically: May 8, 2012
MathSciNet review: 2983030
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Abstract: In this paper, we investigate Jacobi quasi-orthogonal approximation and generalized Jacobi-Gauss-Lobatto interpolation. We also propose Laguerre quasi-orthogonal approximation and generalized Laguerre-Gauss-Radau interpolation. A series of sharp results on these approximations are established, which are applicable to spectral and pseudospectral methods for mixed nonhomogeneous boundary value problems of high order.

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Additional Information

Guo Ben-yu
Affiliation: Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China – and – Scientific Computing Key Laboratory of Shanghai Universities, Division of Computational Science of E-institute of Shanghai Universities

Sun Tao
Affiliation: Department of Applied Mathematics, Shanghai Finance University, Shanghai, 201209, China

Zhang Chao
Affiliation: Department of Mathematics, Xuzhou Normal University, Xuzhou, 221116, China

Keywords: Jacobi quasi-orthogonal approximations, Jacobi-Gauss-Lobatto interpolation, Laguerre quasi-orthogonal approximation, Laguerre -Gauss-Radau interpolation.
Received by editor(s): November 17, 2009
Received by editor(s) in revised form: August 17, 2011
Published electronically: May 8, 2012
Additional Notes: The work of this author is supported in part by NSF of China N. 11171227, Fund for Doctor Degree Authority of Chinese Educational Ministry N. 20080270001, Shanghai Leading Academic Discipline Project N. S30405 and Fund for E-institute of Shanghai Universities N. E03004.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.