Lg. Olson et Rd. Throne, COMPUTATIONAL ISSUES ARISING IN MULTIDIMENSIONAL ELLIPTIC INVERSE PROBLEMS - THE INVERSE PROBLEM OF ELECTROCARDIOGRAPHY, Engineering computations, 12(4), 1995, pp. 343-356
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.