Class Chebspsec

Chebspec Matrix CHEBSPEC Chebyshev spectral differentiation matrix. C = CHEBSPEC(N, K) is a Chebyshev spectral differentiation matrix of order N. K = 0 (the default) or 1. For K = 0 (`no boundary conditions'), C is nilpotent, with C^N = 0 and it has the null vector ONES(N,1). C is similar to a Jordan block of size N with eigenvalue zero. For K = 1, C is nonsingular and well-conditioned, and its eigenvalues have negative real parts. For both K, the computed eigenvector matrix X from EIG is ill-conditioned (MESH(REAL(X)) is interesting).

References: C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin, 1988; p. 69. L.N. Trefethen and M.R. Trummer, An instability phenomenon in spectral methods, SIAM J. Numer. Anal., 24 (1987), pp. 1008-1023. D. Funaro, Computing the inverse of the Chebyshev collocation