Description
Find the first exact node equal to x.
Newton and Neville interpolation build polynomial values from node differences and previous coefficients. Repeated nodes use derivative information rather than ordinary division by zero.
Find the first exact node equal to x.
When to use this tool
Use Newton Basis Zero Factor Witness when you need one explicit divided-difference or polynomial-basis term.
How to use the tool and how it works
- Enter 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 zero, index. Inspect zero before interpreting the associated values.
Find the first exact node equal to x. Return zero true and that index, otherwise false and -1.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| x | X | Required. Finite number. |
| nodes | Nodes | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| zero | Zero | Required. Boolean. |
| index | Zero-based position or diagnostic index under the calculation above; inspect any sentinel policy. | Required. Safe integer. |
json
{
"input": {
"x": 2,
"nodes": [
0,
1,
2
]
},
"output": {
"zero": true,
"index": 2
}
}Limitations and assumptions
- This checks an exact zero factor in a Newton basis, without multiplying factors or applying a numerical tolerance.
- 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.
- Impulse Basis Node Exactvalue Label
Validate node and basis indices within count 1-256.