V2EX tridiagonalization

Tridiagonalization

释义 Definition

三对角化:在线性代数与数值计算中,把一个(通常为对称/厄米)矩阵通过相似变换(如 Householder 变换或 Lanczos 方法)化为三对角矩阵(主对角线及其上下各一条对角线非零)的过程,常用于求特征值/特征向量以提高计算效率。(在更广义情形也可指将矩阵化为三对角结构的过程。)

发音 Pronunciation (IPA)

/tradanlazen/

例句 Examples

Tridiagonalization makes eigenvalue calculations faster.
三对角化会让特征值计算更快。

In many algorithms for symmetric matrices, tridiagonalization is performed first, and then a specialized routine computes eigenvalues from the resulting tridiagonal matrix.
在许多针对对称矩阵的算法中,会先进行三对角化,然后用专门的程序从得到的三对角矩阵计算特征值。

词源 Etymology

由 **tri-**(三)+ diagonal(对角线)+ -ize(使成为……)+ -ation(名词后缀,表示过程/结果)构成,字面意思就是“使之成为三对角形式的过程”。该词主要在数值线性代数语境中使用。

相关词 Related Words

文学与作品 Literary Works

  • Matrix Computations(Golub & Van Loan)
  • Numerical Linear Algebra(Lloyd N. Trefethen & David Bau III)
  • Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide(Bai, Demmel, Dongarra, Ruhe, van der Vorst 等)
  • 经典特征值算法相关论文与资料中(如介绍 LanczosHouseholder 方法的文献)常出现该术语
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