Abstract
Spectral collocation approximations based on Legendre-Gauss-Lobatto nodes is considered. The collocation method is settled in a variational form, starting from the weak formulation of the differential problem. Numerical approximations to first and second order operators are introduced and the behavior of their discrete eigenvalues is studied. A finite element preconditioner for second order problems is proposed. Several numerical results concerning the condition number of the preconditioned spectral matrices and the application to conjugate gradient iterations are reported.
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Zampieri, E. On the condition number of some spectral collocation operators and their finite element preconditioning. J Sci Comput 9, 419–443 (1994). https://doi.org/10.1007/BF01575101
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DOI: https://doi.org/10.1007/BF01575101