How (Un)stable Are Vandermonde Systems?
How (Un)stable Are Vandermonde Systems?
复制标题
Vandermonde 系统有多（不稳定）稳定？
DOI：
10.1201/9781003072584-9
复制
发表时间：
2020
期刊：
影响因子：
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通讯作者：
W. Gautschi
中科院分区：
文献类型：
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作者：
W. Gautschi
应用和数值分析中的许多问题最终归结为求解大型线性代数方程组。由于这种系统的矩阵和右手边通常是（有时是大量的）计算的结果，它们受到不可避免的噪声水平的影响，这些噪声水平是由它们生成过程中的舍入误差引起的。因此，试图估计这种不确定性对系统解的影响是一个实际问题。一个共同的答案和一个我们将采取在续集有关任何非奇异系统
Many problems in applied and numerical analysis eventually boil down to solving large systems of linear algebraic equations. Since the matrices and right-hand sides of such systems are typically the result of (sometimes extensive) computations, they are subject to an unavoidable level of noise caused by the rounding errors committed during their generation. It is then a matter of practical concern trying to estimate the effect of such uncertainties upon the solution of the system. A common answer and one which we shall adopt in the sequel concerning any nonsingular system