ON POSITIVE SYMMETRIZABLE MATRICES AND PRE-SYMMETRY ITERATION ALGORITHMS
正定可对称化矩阵与预对称迭代算法

Second order elliptic equation is a class of mathematical model for scientific computing, such as convex-diffusion, oil-reservoir simulation, etc. Based on intrinsic symmetrizable property, a new concept on positively symmetrizable matrix is proposed in this paper. We point that for such kind of equation systems, it is possible to adopt special preconditioning CG algorithm, e.g. 1]-3], instead of the usual iteration procedure for general non-symmetry systems, such as GMRES 3]-4] ) BiCGSTAB 5]. Numerical tests show the new algorithm is effective for solving this kind of second order elliptic discrete systems.