Description
Require nonzero commonScale, multiply one weight by it, and return invariant true.
Barycentric interpolation expresses a polynomial as a quotient of weighted sums. Standard weights depend on node differences; common nonzero scaling cancels only when applied consistently to the full quotient.
Require nonzero commonScale, multiply one weight by it, and return invariant true.
When to use this tool
Use Barycentric Node Weight Common Scale Invariance when you need one barycentric weight, sign, or influence component.
How to use the tool and how it works
- Enter weight, commonScale. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read scaledWeight, invariant. Inspect invariant before interpreting the associated values.
Require nonzero commonScale, multiply one weight by it, and return invariant true.1
In the barycentric quotient, the same weights appear in the numerator and denominator. A common nonzero multiplier cancels across the complete formula; changing only one node weight generally does not.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| weight | Weight | Required. Finite number. |
| commonScale | Common Scale | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| scaledWeight | Scaled Weight | Required. Finite number. |
| invariant | Invariant | Required. Boolean. |
{
"input": {
"weight": 2,
"commonScale": -3
},
"output": {
"scaledWeight": -6,
"invariant": true
}
}Limitations and assumptions
- Invariance concerns the complete barycentric quotient only when every weight shares that scale; this tool does not verify or evaluate the full quotient.
- 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
Use a complete barycentric evaluator with exact-node handling and appropriate weight scaling for actual interpolation.
References
-
Calculation and input contract: interpolation/barycentric-node-weight-common-scale-invariance — tool.io
-
Barycentric Lagrange Interpolation — Jean-Paul Berrut and Lloyd N. Trefethen / SIAM Review
Similar or alternative tools
- Barycentric Weight Node Deletion Factor
Require node different from deletedNode and multiply weight by node - deletedNode for newWeight.
- Barycentric Single Node Influence Ratio
At an exact node hit return one for that selected node and zero for others; otherwise normalize selected weight/(x-node) by the sum of all such terms.