论文标题
高斯 - 约旦消除和错误分析的明确公式
The explicit formula for Gauss-Jordan elimination and error analysis
论文作者
论文摘要
高斯 - 约旦消除程序的连续中间矩阵的元素的明确公式将线性方程系统解决方案应用于误差分析。根据相对不确定性和决定因素的大小，稳定条件的范围是使高斯 - 约旦程序导致尊重右手成员中原始不确定的解决方案。该解决方案与Cramer规则给出的相同。不确定是由标量中性物质建模的，标量中性数是（非标准）实数的凸组。由此产生的计算规则扩展了非正式错误演算，并允许在每个阶段跟踪错误。
The explicit formula for the elements of the successive intermediate matrices of the Gauss-Jordan elimination procedure for the solution of systems of linear equations is applied to error analysis. Stability conditions in terms of relative uncertainty and size of determinants are given such that the Gauss-Jordan procedure leads to a solution respecting the original imprecisions in the right-hand member. The solution is the same as given by Cramer's Rule. Imprecisions are modelled by scalar neutrices, which are convex groups of (nonstandard) real numbers. The resulting calculation rules extend informal error calculus, and permit to keep track of the errors at every stage.
