Accuracy and Stability of Numerical Algorithms¶
Nicholas J. Higham, A., & Stability of Numerical Algorithms, 2. e. (. (2002). Accuracy and Stability of Numerical Algorithms.
Cited by¶
7 citations across 7 artifacts.
Each citation links to the sentence it supports in the citing article.
Domain-specific¶
- Condition Number
- Numerical Method
- Listed in the references but not attached to a specific claim.
- Significant figures
Mechanisms¶
- Basis Conditioning and Perturbation Audit
- Its subtlety is that conditioning is relative to scaling and norm: a frightening condition number is sometimes an artifact of un-normalized units (metres mixed with microns), fixable by rescaling rather than by redesigning the basis — so the audit can raise false alarms if run on raw, unscaled generators.
This sourceShows that condition numbers depend on the chosen norm and can sometimes be reduced through appropriate row or column scaling.
- Its subtlety is that conditioning is relative to scaling and norm: a frightening condition number is sometimes an artifact of un-normalized units (metres mixed with microns), fixable by rescaling rather than by redesigning the basis — so the audit can raise false alarms if run on raw, unscaled generators.
- Condition-Number Dashboard
- Its failure modes start with scale: κ is scale-dependent, so a careless unit choice can inflate or deflate it and a fixed normalization policy is mandatory
This sourceShows that measurement units and row scaling can change a matrix condition number dramatically.
- Its failure modes start with scale: κ is scale-dependent, so a careless unit choice can inflate or deflate it and a fixed normalization policy is mandatory
- Gaussian Elimination Pivot Check
- On measured data it is brittle: naive elimination is numerically unstable
This sourceExplains the numerical-instability risk of Gaussian elimination without pivoting and the stabilizing role of partial pivoting.
- On measured data it is brittle: naive elimination is numerically unstable
- Uncertainty Propagation Calculation
- It flags the dangerous cases, especially the subtraction of nearly-equal quantities, where a tiny input error becomes a catastrophic output error, and it tells you which input to tighten to shrink the result.
This sourceExplains how subtracting nearly equal quantities can amplify small input errors into large relative error in the computed difference.
- It flags the dangerous cases, especially the subtraction of nearly-equal quantities, where a tiny input error becomes a catastrophic output error, and it tells you which input to tighten to shrink the result.
Verification¶
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Does it back the claim? Not recorded. Neither this nor any other of the 7 citations of this work carries a recorded support check.
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Registry ID ref:66814e5cb601 · see in the full table