Description
Multiply coefficient by the product of x minus each node for term.
Newton and Neville interpolation build polynomial values from node differences and previous coefficients. Repeated nodes use derivative information rather than ordinary division by zero.
Multiply coefficient by the product of x minus each node for term.
When to use this tool
Use Newton Divided Difference Append Term when you need one explicit divided-difference or polynomial-basis term.
How to use the tool and how it works
- Enter coefficient, x, nodes. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read term. Use the output convention below.
Multiply coefficient by the product of x minus each node for term. An empty node list has product one.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coefficient | Supplied coefficient for the indicated basis or model term. | Required. Finite number. |
| x | X | Required. Finite number. |
| nodes | Nodes | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| term | Single mathematical contribution; aggregation and normalization are separate. | Required. Finite number. |
{
"input": {
"coefficient": 2,
"x": 3,
"nodes": [
0,
1
]
},
"output": {
"term": 12
}
}Limitations and assumptions
- This forms one Newton-basis contribution rather than updating the coefficient table or summing a complete interpolant.
- 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 Basis Zero Factor Witness
Find the first exact node equal to x.
- Neville Single Table Cell Update
Combine leftValue and rightValue with the two Neville weights at x and divide by leftNode - rightNode.