V2EX conjugate gradient

Conjugate Gradient

释义 Definition

共轭梯度(法):一种常用的迭代算法,主要用于求解大型稀疏的对称正定线性方程组 \(Ax=b\),也可用于无约束优化中沿“共轭方向”逐步逼近最优解。常见搭配:conjugate gradient method / CG

发音 Pronunciation (IPA)

/kndt redint/

例句 Examples

We used conjugate gradient to solve the equation.
我们用共轭梯度法来解这个方程。

For large sparse symmetric positive definite matrices, conjugate gradient often performs well, especially with an effective preconditioner.
对于大型稀疏的对称正定矩阵,共轭梯度法通常表现很好,尤其是在配合有效的预条件器时。

词源 Etymology

conjugate 源自拉丁语 conjugare(“结合、成对连接”),在数学里引申为“共轭的/相互配对的”。gradient 来自拉丁语 gradus(“步、级、梯度”),在数学中指函数变化最快的方向(梯度)。合起来强调:算法每一步选择的搜索方向彼此“共轭”(相对某个矩阵内积正交),从而提高收敛效率。

相关词 Related Words

文学与著作 Literary Works

  • Methods of Conjugate Gradients for Solving Linear Systems(Hestenes & Stiefel,1952)
  • Matrix Computations(Gene H. Golub & Charles F. Van Loan)
  • Iterative Methods for Sparse Linear Systems(Yousef Saad)
  • Numerical Recipes(Press 等)
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