COMPUTATIONAL ISSUES ARISING IN MULTIDIMENSIONAL ELLIPTIC INVERSE PROBLEMS - THE INVERSE PROBLEM OF ELECTROCARDIOGRAPHY

We compare a recently proposed generalized eigensystem approach and a new modified generalized eigensystem approach to more widely used trun cated singular value decomposition and zero-order Tikhonov regularizat ion for solving multidimensional elliptic inverse problems. As a test case, we use a finite element representation of a homogeneous eccentri c spheres model of the inverse problem of electrocardiography. Special attention is paid to numerical issues of accuracy, convergence, and r obustness. While the new generalized eigensystem methods are substanti ally more demanding computationally, they exhibit improved accuracy an d convergence compared with widely used methods and offer substantiall y better robustness.