V2EX sor method

Sor Method

释义 Definition

SOR method(Successive Over-Relaxation method,逐次超松弛法)是一种用于求解线性方程组(尤其是由偏微分方程离散化得到的稀疏线性系统)的迭代算法。它通常被看作 GaussSeidel(高斯-赛德尔)迭代的加速版本,通过引入“松弛因子” \( \omega \) 来加快收敛;当 \( \omega=1 \) 时退化为 GaussSeidel。除这一常见含义外,SOR 在其他领域也可能代表别的缩写。

发音 Pronunciation (IPA)

/s o r mθd/

例句 Examples

I used the SOR method to solve the linear system.
我用 SOR 方法来求解这个线性方程组。

With an appropriate relaxation factor, the SOR method can converge much faster than GaussSeidel for large sparse matrices arising from PDE discretization.
选择合适的松弛因子后,对于由偏微分方程离散化产生的大型稀疏矩阵,SOR 方法的收敛速度往往比高斯-赛德尔法快得多。

词源 Etymology

“SOR”是首字母缩略词,来自 Successive Over-Relaxation:successive(逐次的)强调逐步迭代更新,over-relaxation(超松弛)指引入松弛参数对更新幅度进行“放大/调节”,以期获得更快的收敛速度;“method”意为方法。

相关词 Related Words

文学与经典著作中的用例 Literary Works

  • Iterative Methods for Sparse Linear Systems(Yousef Saad)
  • Matrix Iterative Analysis(Richard S. Varga)
  • Numerical Linear Algebra(Lloyd N. Trefethen & David Bau III)
  • Numerical Recipes(Press 等)
  • Numerical Linear Algebra(Gene H. Golub & Charles F. Van Loan)
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