Description
Return the reciprocal product of selected-node minus every other node.
Lagrange basis functions equal one at their own node and zero at the other distinct nodes. Their weighted sum interpolates node values, but closely spaced nodes can create numerical sensitivity.
Return the reciprocal product of selected-node minus every other node.
When to use this tool
Use Lagrange Basis Leading Coefficient when you need one polynomial basis weight or residual.
How to use the tool and how it works
- Enter nodes, index. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read coefficient. Use the output convention below.
Require a nonempty distinct node set and valid index. Return the reciprocal product of selected-node minus every other node.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| nodes | Nodes | Required. Array of finite number; maximum items 256. |
| index | Zero-based position or diagnostic index under the calculation above; inspect any sentinel policy. | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| coefficient | Supplied coefficient for the indicated basis or model term. | Required. Finite number. |
{
"input": {
"nodes": [
0,
1,
2
],
"index": 1
},
"output": {
"coefficient": -1
}
}Limitations and assumptions
- This is a leading basis coefficient and standard barycentric weight; close nodes can make it poorly conditioned and no rescaling is applied.
- 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 stable full interpolation evaluator and inspect node conditioning before relying on high-order or extrapolated values.
References
Similar or alternative tools
- Interpolation: Barycentric Node Weight Sign
Return +1 when the number of nodes to its right is even and -1 when odd.
- Barycentric Weight Node Deletion Factor
Require node different from deletedNode and multiply weight by node - deletedNode for newWeight.