Practice question · Multiple choice
A condition number of 10⁸ is reported for a linear system solved in double precision, which carries about 16 digits. What should you conclude about the answer?
Hints
- The condition number multiplies relative error. Start with 10⁻¹⁶ and multiply.
- Ask whether this is a statement about the algorithm or about the problem.
Show the answer
C. That roughly half its digits may be meaningless
Why
Multiply 10⁻¹⁶ by 10⁸ and you have relative error around 10⁻⁸, about eight trustworthy digits. It describes the problem rather than the method, so a better algorithm will not recover the rest; what it buys you is knowing how much of the printout to believe.
Practise Solving Linear Systems Numerically
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