Description
Use occurrenceIndex as derivativeOrder and divide derivativeValue by occurrenceIndex factorial for dividedDifferenceValue.
Newton and Neville interpolation build polynomial values from node differences and previous coefficients. Repeated nodes use derivative information rather than ordinary division by zero.
Use occurrenceIndex as derivativeOrder and divide derivativeValue by occurrenceIndex factorial for dividedDifferenceValue.
When to use this tool
Use Interpolation: Repeated Node Derivative Label when you need one explicit divided-difference or polynomial-basis term.
How to use the tool and how it works
- Enter occurrenceIndex, derivativeValue. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Use occurrenceIndex as derivativeOrder and divide derivativeValue by occurrenceIndex factorial for dividedDifferenceValue. Orders are 0-32.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| occurrenceIndex | Occurrence Index | Required. Safe integer. |
| derivativeValue | Derivative Value | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
| result.derivativeOrder | Derivative Order | Calculated result member: number. |
| result.dividedDifferenceValue | Divided Difference Value | Calculated result member: number. |
{
"input": {
"occurrenceIndex": 2,
"derivativeValue": 6
},
"output": {
"result": {
"derivativeOrder": 2,
"dividedDifferenceValue": 3
}
}
}Limitations and assumptions
- This is a repeated-node confluent divided-difference term; the supplied derivative must use the matching coordinate and order.
- Outputs are nested inside result. 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
Validate the complete node/value table and use a stable interpolation algorithm for a full polynomial evaluation.
References
Similar or alternative tools
- Newton Divided Difference Append Term
Multiply coefficient by the product of x minus each node for term.
- Neville Single Table Cell Update
Combine leftValue and rightValue with the two Neville weights at x and divide by leftNode - rightNode.