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Here, the authors used a previously proposed model problem to examine the effects of inhomogeneities on four techniques for numerically solving the inverse problem of electrocardiography. The layered inhomogeneous eccentric spheres system contains three regions representing the lungs, muscle, and subcutaneous fat, and is numerically modeled using finite elements. The authors simulated both anterior and posterior spherical cap activation fronts. They examined inverse solutions based on zero order Tikhonov regularization, truncated singular value decomposition, their new generalized eigensystem approach, and a modification of the generalized eigensystem approach. The effects on the inverse solutions of geometrical errors, errors in the assumed conductivities, and homogeneous torso assumptions were examined.