¹Taiyuan Normal University, Taiyuan 030012, P.R.C.
²Class 390614, School of Computer Science and Engineering, Beihang University, Beijing 100191, P. R. China

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Abstract—We present the convergent splitting and convergent multisplitting for linear system of algebraic equations Ax = b when the coefficient matrix is a non-hermitian positive definite matrix. Furthermore, we also establish the comparison theorems of different splittings or multisplittings based on numerical radius. Mainly, we propose two new selfadaptive multisplitting parallel methods which the weighting matrices are self-adaptive. Finally, we give an application to solve the two- dimensional advection-diffusion equations.

Index Terms—Non-hermitian matrix, positive definite matrix, multisplitting, comparison theorem

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Cite: Chuan-Long Wang, Yan-Ping Wang,and Jin Wang "The Self-Adaptive Multi-Splitting Parallel Methods for Non-Hermitian Positive Definite Systems," Journal of Software vol. 7, no. 11, pp. 2400-2404, 2012.