Hassell, Andrew; Barnett, Alexander
We consider the "Method of particular solutions" for numerically computing eigenvalues and eigenfunctions of the Laplacian�?�on a smooth, bounded domain Omega in RR^n with either Dirichlet or Neumann boundary conditions. This method constructs approximate eigenvalues E, and approximate eigenfunctions u that satisfy�?u=Eu�in Omega, but not the exact boundary condition. An inclusion bound is then an estimate on the distance of E from the actual spectrum of the Laplacian, in terms of (boundary...[Show more]
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