V2EX band matrix

Band Matrix

Definition / 定义

带状矩阵:一种稀疏矩阵,其非零元素主要集中在主对角线及其两侧的若干条对角线“带状区域”内;带宽以主对角线两侧允许出现非零元的范围来衡量。(在数值计算中常用于提高存储与求解效率。)

Pronunciation / 发音

/bnd metrks/

Examples / 例句

A band matrix can be stored efficiently because most entries are zero.
带状矩阵可以高效存储,因为大多数元素为零。

When solving a large system of equations, exploiting the band matrix structure can greatly reduce computation time and memory use.
在求解大型方程组时,利用带状矩阵的结构可以显著降低计算时间和内存消耗。

Etymology / 词源

band 原意是“带、条带”,用于描述矩阵中非零元素沿主对角线形成的“带状”分布;matrix 源自拉丁语 matrix(“母体、来源”),在数学里引申为“矩阵”。该术语在数值线性代数与工程计算中常见。

Related Words / 相关词汇

Literary Works / 文学作品举例

  • Gene H. Golub & Charles F. Van Loan, Matrix Computations(讨论带状/稀疏矩阵的存储与算法)
  • Lloyd N. Trefethen & David Bau III, Numerical Linear Algebra(涉及带状结构在线性方程求解中的应用)
  • James W. Demmel, Applied Numerical Linear Algebra(介绍利用带状结构提升计算效率的思想)
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