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arXiv 0907.2397math.HOcs.NAmath.NA
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普通消元法如何变成高斯消元法

How Ordinary Elimination Became Gaussian Elimination

Joseph F. Grcar

AI总结:

本文追溯了线性方程组消元法从牛顿笔记到高斯命名,再到矩阵描述的历史演变,分析了高斯消元法名称的由来。

摘要:

牛顿在他宁愿不被发表的笔记中描述了一种解联立方程的方法,后来的作者将其专门应用于线性方程。这种方法——欧拉不推荐,勒让德称之为“普通的”,高斯称之为“常见的”——现在以高斯命名:“高斯”消元法。高斯的名字与消元法相关联,是通过专业计算人员采用高斯为他自己最小二乘计算设计的专门符号。这种符号使得消元法可以被视为一系列算术运算,这些运算不断针对手算进行优化,最终由矩阵描述。

英文摘要:

Newton, in notes that he would rather not have seen published, described a process for solving simultaneous equations that later authors applied specifically to linear equations. This method that Euler did not recommend, that Legendre called "ordinary," and that Gauss called "common" - is now named after Gauss: "Gaussian" elimination. Gauss's name became associated with elimination through the adoption, by professional computers, of a specialized notation that Gauss devised for his own least squares calculations. The notation allowed elimination to be viewed as a sequence of arithmetic operations that were repeatedly optimized for hand computing and eventually were described by matrices.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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