Title: Efficient Spectral-Galerkin Method II. Direct Solvers of Second
        and Fourth Order Equations by Using Chebyshev Polynomials

Author: Jie Shen

Status: SIAM J. Sci. Comput. 16, 74-87, 1995

Abstract:

Efficient direct solvers based on the Chebyshev-Galerkin methods for
second and fourth order equations are  presented. They are based on
appropriate base functions for the Galerkin formulation which lead to
discrete systems with special structured matrices which can be
efficiently inverted. Numerical results indicate that the direct
solvers presented in this paper are significantly more accurate and efficient
than that based on the Chebyshev-tau method.