linear equation system $Ax=b$ and reliable digits verification?

Example: the linear equation system $Ax=b$ has one approximation $\bar x$ and one exact $x^* \neq 0$ solutions. we also gives: $p>3, ||x^* - \bar x || \leq 10^{-20} + ||A|| ||A^{-1}|| 10^{-p} ||x^*|| $ which $||A|| ||A^{-1}||=10^{-4}$. The reliable digits of $\bar x$ for solutions of this system of equation is $0$.

Question: this example takes from my notes on Numerical Methods Course that adopted from one math contest. I need to verify this question via Math Tools, like as Mathematica. I ran into a challenge that there is a typo in this question and the estimation should be $10^4$ not $10^{-4}$ to get zero solution. is there anyway to check it via Wolfram? can this tools detects the error in this example?


Category: equation solving Time: 2016-07-30 Views: 0

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