A multiresolution strategy for reduction of elliptic PDEs and eigenvalue problems (Q1267268)

The paper in hand is a continuation of [\textit{M. E. Brewster} and \textit{G. Beylkin}, Appl. Comput. Harmon. Anal. 2, 327-349 (1995; Zbl 0840.65047)] and deals with the multiresolution strategy for the reduction of elliptic partial differential equations. This strategy serves as a method for describing the behaviour of the solution when considering the change of coefficients of the underlying differential equation on some coarse scale, only. For this, high-order wavelets rather than the Haar bsis is used. This, in addition, allows the development of efficient numerical methods. The authors prove that the reduced differential operator is compressible in wavelet bases and the spectral bounds for the reduced operator on all scales coincide with those of the original self-adjoint, strictly elliptic operator. The paper finishes with a numerical example.