Description
Combine leftValue and rightValue with the two Neville weights at x and divide by leftNode - rightNode.
Newton and Neville interpolation build polynomial values from node differences and previous coefficients. Repeated nodes use derivative information rather than ordinary division by zero.
Combine leftValue and rightValue with the two Neville weights at x and divide by leftNode - rightNode.
When to use this tool
Use Neville Single Table Cell Update when you need one explicit divided-difference or polynomial-basis term.
How to use the tool and how it works
- Enter x, leftNode, rightNode, leftValue, rightValue. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read value. Use the output convention below.
Require distinct leftNode and rightNode. Combine leftValue and rightValue with the two Neville weights at x and divide by leftNode - rightNode.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| x | X | Required. Finite number. |
| leftNode | Left Node | Required. Finite number. |
| rightNode | Right Node | Required. Finite number. |
| leftValue | Left Value | Required. Finite number. |
| rightValue | Right Value | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| value | Value | Required. Finite number. |
{
"input": {
"x": 1,
"leftNode": 0,
"rightNode": 2,
"leftValue": 0,
"rightValue": 4
},
"output": {
"value": 2
}
}Limitations and assumptions
- The values must represent the matching previous table cells; this computes one update without checking a whole interpolation table.
- 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
- Interpolation: Repeated Node Derivative Label
Use occurrenceIndex as derivativeOrder and divide derivativeValue by occurrenceIndex factorial for dividedDifferenceValue.
- Newton Divided Difference Append Term
Multiply coefficient by the product of x minus each node for term.