Description
Return a local relative condition number from a derivative.
Differential-calculus formulas relate supplied local values and derivatives under explicit coordinate and unit conventions. A tangent term, curvature expression or directional derivative assumes the required differentiability and regularity; substituting numerical derivatives does not verify those hypotheses for an actual function.
Return a local relative condition number from a derivative.
When to use this tool
Use Local Relative Condition Number From Derivative when evaluating the stated local differential-calculus identity from supplied values.
How to use the tool and how it works
- Enter inputValue, outputValue, derivative. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read condition. Use the output convention below.
Return a local relative condition number from a derivative. Require outputValue != 0; condition = abs(inputValue*derivative/outputValue).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| inputValue | Input Value | Required. Finite number. |
| outputValue | Output Value | Required. Finite number. |
| derivative | Derivative | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| condition | Condition | Required. Finite number. |
{
"input": {
"inputValue": 2,
"outputValue": 4,
"derivative": 4
},
"output": {
"condition": 2
}
}Limitations and assumptions
- This is scalar first-order relative sensitivity, not an interval error bound, full algorithmic stability or a multidimensional condition estimate.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Differentiate or validate the complete function and its domain first; use suitable symbolic or numerical methods and check regularity and coordinate conventions for the intended interpretation.
References
Similar or alternative tools
- Derivative Relative Condition Term
Return signed relative sensitivity and absolute condition.
- Euler Homogeneity Local Residual
Return Euler homogeneity residual at supplied values.