Practice question · Numerical answer
A standard bound says the relative error in the solution can be as large as the condition number times the relative error in the data. With a condition number of 500 and data whose relative error is 0.0002, what is the largest relative error the solution may carry?
Hints
- Multiply the two quantities given.
- 500 times 0.0002.
Show the answer
0.1 (answers within ±0.001 count)
Why
500 * 0.0002 = 0.1, a 10% possible error from data accurate to two parts in ten thousand. The condition number is exactly this amplification factor, which is why it, and not the solver, sets the ceiling on achievable accuracy.
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