V2EX tridiagonal matrix

Tridiagonal Matrix

Definition / 释义

三对角矩阵:一种特殊的方阵,除主对角线及其上、下相邻的两条对角线外,其余元素都为 0。常见于数值计算中(如差分法离散后的线性方程组),可用高效算法求解。

Pronunciation / 发音(IPA)

/tradanl metrks/

Examples / 例句

A tridiagonal matrix is easy to store and compute with.
三对角矩阵很容易进行存储和计算。

After discretizing the second-order differential equation, we obtain a tridiagonal matrix system that can be solved efficiently by the Thomas algorithm.
将二阶微分方程离散化后,会得到一个三对角矩阵方程组,可用托马斯算法高效求解。

Etymology / 词源

tridiagonaltri-(“三”)+ diagonal(“对角线的”)构成,字面意思是“有三条对角线(非零带)的”。matrix 源自拉丁语 matrix(“母体、来源”),在数学中引申为“矩阵”,即按行列排列的数表。

Related Words / 相关词汇

Literary Works / 文献与著作中的常见出处

  • Gene H. Golub & Charles F. Van Loan, Matrix Computations(讨论三对角化与相关高效计算)
  • Lloyd N. Trefethen & David Bau III, Numerical Linear Algebra(包含三对角矩阵与特征值算法)
  • William H. Press et al., Numerical Recipes(介绍三对角线性方程组的快速解法)
  • Richard L. Burden & J. Douglas Faires, Numerical Analysis(差分法与三对角线性系统的应用)
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