Quadrant Tridiagonal Partitioning and Preconditioned Conjugate Gradient Method for Solving Elliptic Problems
Quadarant diagonal partitioning (QDP) method is an iterative method for solving linear system proposed by D. J. Evans et al. (see ,,) appropriate for paralell implementation. Here we show that in case of second order elliptic problem, the classical, color and multicolor ordering technique  are applicable for further paralellization of QDP iterative methods. Moreover we give a direct algorithm with arithmetical complexity O(n) for solving a special quadrant tridiagonal matrix and using these results we propose a quadrant tridiagonal preconditioned (QTP) conjugate gradient method for solving second order elliptic problems. The numerical experiments presented here shows that this method in several cases are more effective than other PCG algorithm.
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