International Conference on Information Technology and Computer Science, 3rd (ITCS 2011)
16 Alternating Lower-Upper Splitting Iterative Method for Positive Definite Linear Systems
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Large scale positive definite linear systems appear in many areas of science and engineering. A new iterative approach, which is an alternating direction implicit(ADI)—type method, is proposed in this paper. The coefficient matrix is split into a lower and an upper triangular matrices, therefore the new method is termed as the alternating lower-upper splitting (ALUS) iterative method. The convergence theorems of the ALUS method are established. With less amount of computational cost, the CPU time can be greatly diminished. Analysis and numerical tests demonstrate the new method is efficient and robust. All the results illustrate the ALUS method performs well for positive definite systems.