an:01282757
Zbl 0924.65077
Dawkins, Paul T.; Dunbar, Steven R.; Douglass, Rod W.
The origin and nature of spurious eigenvalues in the spectral tau method
EN
J. Comput. Phys. 147, No. 2, 441-462 (1998).
00053907
1998
j
65L15 65L10 34L15 65L60 34B05
Lanczos tau method; series expansions; orthogonal functions; Chebyshev-tau spectral method; spurious eigenvalues; generalized eigenvalue problem
The tau method, first proposed by Lanczos, is a means of solving boundary value problems for ordinary differential equations using truncated series expansions in a complete set of orthogonal functions. From the author's summary: `The Chebyshev-tau spectral method for approximating eigenvalues of boundary value problems may produce spurious eigenvalues with large positive real parts, even when all true eigenvalues of the problem are known to have negative real parts. We explain the origin and nature of the `spurious eigenvalues' in an example problem. The explanation will demonstrate that the large positive eigenvalues are an approximation of infinite eigenvalues in a nearby generalized eigenvalue problem'.
W.Velte (W??rzburg)