Analysis of a Preconditioned CG method for an Inverse Bioelectric Field Problem

This paper is a continuation of our previous analysis from [4] related to the electrocardiographic (ECG) inverse problem. In that paper we formulated the inverse ECG problem as a differential inverse problem and derived an appropriate simulation procedure. As numerical solver we employed the Conjugate Gradient algorithm for the normal equations (CGNE) together with a stopping test constructed following the discrepancy principle by Morozov. In the current paper we consider a preconditioned version of the CGNE algorithm. The preconditioner is constructed using the Cholesky factors of the discrete Laplacian which forms a block of the original system matrix. We derive some theoretical results concerning the efficiency and also the limitations of the preconditioner. Numerical experiments and comparisons are presented for the cases analysed in [4]. [4] M. Mohr, C. Popa and R. Rüde, A Differential Inverse Problem from Cardiac Imaging, Proceedings of the Third Workshop on Mathematical Modelling of Environmental and Life Sciences Problems, Constanta, Romania, 27-30 May 2004; Editura Academiei Romane, Bucuresti 2004, 189-204.

@inproceedings{id731,
  author = {Mohr, M. and Popa, C. and R\"ude, U.},
  booktitle = {Proceedings of the Fourth Workshop on Mathematical Modelling of Environmental and Life Sciences Problems},
  editor = {Ion, S. and Marinoschi, G. and Popa, C.},
  language = {en},
  pages = {135-146},
  publisher = {Editura Academiei Rom\^ane},
  series = {Series on Mathematical Modelling of Environmental and Life Sciences Problems},
  title = {Analysis of a Preconditioned CG method for an Inverse Bioelectric Field Problem},
  year = {2006},
}

%O Conference Proceedings
%A Mohr, M.
%A Popa, C.
%A Rüde, U.
%B Proceedings of the Fourth Workshop on Mathematical Modelling of Environmental and Life Sciences Problems
%E Ion, S.
%E Marinoschi, G.
%E Popa, C.
%G en
%P 135-146
%I Editura Academiei Române
%S Series on Mathematical Modelling of Environmental and Life Sciences Problems
%T Analysis of a Preconditioned CG method for an Inverse Bioelectric Field Problem
%D 2006