How Accurate is inv(A)*b?
How Accurate is inv(A)*b?
复制标题
inv(A)*b 有多准确？
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Sivan Toledo
中科院分区：
文献类型：
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作者：
Alex Druinsky;Sivan Toledo
几本广泛使用的教科书使读者相信，通过将向量B乘以计算的逆inv（A）来求解线性方程组Ax = B是不准确的。几乎所有其他教科书的数值分析和数值线性代数建议不要使用计算逆没有说明这是否是准确的或不。事实上，在关于如何计算逆的合理假设下，x = inv（A）*B与最佳向后稳定求解器计算的解一样精确。这一事实并不新鲜，但显然令人费解。我们回顾了文献的准确性，这种计算，并提出了一个独立的数值分析。
Several widely-used textbooks lead the reader to believe that solving a linear system of equations Ax = b by multiplying the vector b by a computed inverse inv(A) is inaccurate. Virtually all other textbooks on numerical analysis and numerical linear algebra advise against using computed inverses without stating whether this is accurate or not. In fact, under reasonable assumptions on how the inverse is computed, x = inv(A)*b is as accurate as the solution computed by the best backward-stable solvers. This fact is not new, but obviously obscure. We review the literature on the accuracy of this computation and present a self-contained numerical analysis of it.
影响因子：
2.1
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通讯作者：
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