Ill-Conditioned Problem/Examples/Arbitrary Example 1
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Example of Ill-Conditioned Problem
Consider the zeroes of the polynomials:
\(\ds \map p x\) | \(=\) | \(\ds x^8\) | ||||||||||||
\(\ds \map q x\) | \(=\) | \(\ds x^8 - 10^8\) |
The zeroes of $\map p x$ are all $0$.
However, the zeroes of $\map q x$ are all of modulus $0 \cdotp 1$.
Hence, while $\map q x$ is a tiny perturbation of $\map p x$, the zeroes differ by a modulus some $8$ orders of magnitude larger.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): ill-conditioned
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): ill-conditioned