臺灣博碩士論文加值系統

本論文主要探討不完全LU分解之方法，並將其結合預條件化雙共軛梯度法BiCG和BiCGStab用於解大型稀疏線性系統。在實驗中，我們以MATLAB為基礎，研究ILU(p)及ILUT(τ)條件化子對收歛速率與計算時間之影響。

In this thesis, we study the Incomplete LU(ILU) decomposition. Then we use various ILU precondiditoners with BiCG and BiCGStab methods to
solve sparse linear systems. Our experiments based on MATLAB softwares, which apply ILU(p) and ILUT(τ) as preconditioners to solve linear systems.
We compare the convergence rate and computing time for both methods to find at the effect of fill-in level p and the drop tolerance τ.

1 Introduction 1
2 Incomplete LU decomposition 2
3 Conjugate Gradient Methods 17
4 Preconditioning Step 24
5 Numerical Results 29
6 Conclusions 56
References

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