 
Summary: A SPECTRAL METHOD FOR THE EIGENVALUE PROBLEM FOR
ELLIPTIC EQUATIONS
KENDALL ATKINSON AND OLAF HANSEN
Abstract. Let be an open, simply connected, and bounded region in Rd, d 2, and assume
its boundary is smooth. Consider solving the eigenvalue problem Lu = u for an elliptic partial
differential operator L over with zero values for either Dirichlet or Neumann boundary conditions.
We propose, analyze, and illustrate a `spectral method' for solving numerically such an eigenvalue
problem. This is an extension of the methods presented earlier in [5], [6].
Key words. elliptic equations, eigenvalue problem, spectral method, multivariable approxima
tion
AMS subject classification. 65M70
1. INTRODUCTION. We consider the numerical solution of the eigenvalue
problem
Lu(s) 
d
k,=1
sk
ak,(s)
u(s)
