Iterative Solution of Dense Linear Systems Arising from Boundary Element Formulations of the Biomagnetic Inverse Problem
نویسندگان
چکیده
Magnetoencephalography (MEG) is a noninvasive technique for studying neuronal activity in the living human brain. Weak magnetic elds caused by the activity are measured from outside the head. Based on these measurements the source of the activity is located with the help of a mathematical model. A part of the localization is the repeated computation of the electric potential on the surface of the brain caused by a known electric source. In this paper we study the iterative solution of dense linear systems that arise from a boundary element discretization of the potential integral equation. We show that preconditioned iterative methods, such as BI-CGSTAB with the ILU(0) preconditioner, can easily outperform direct solvers for the problem. We also compute analytically the eigenvalues of the integral operator for a spherical model and show how these are approximated by the eigenvalues of the coeecient matrix.
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