Error Estimates for Adaptive Spectral Decompositions

Abstract Adaptive spectral (AS) decompositions associated with a piecewise constant function, u , yield small subspaces where the characteristic functions comprising are well approximated. When combined Newton-like optimization methods for solution of inverse medium problems, AS have proved remarkably efficient in providing at each nonlinear iteration low-dimensional search space. Here, we derive $$L^2$$ L 2 -error estimates decomposition truncated after K terms, when is and consists over Lipschitz domains background. Our apply both to continuous discrete Galerkin finite element setting. Numerical examples illustrate accuracy media that either do, or do not, satisfy assumptions theory.