Examples
Examples
Try the starting example
- Samples: x,y, one pair per line
- 0,1 1,2 2,5
- Query x values
- 0.5,1.5
- Interpolated values in query order
- 1.25, 3.25
- Global polynomial degree
- 2
- Queries outside sampled x range
- 0
Try another scenario
- Samples: x,y, one pair per line
- 0,1 1,2 2,5
- Query x values
- 0,1,2
- Interpolated values in query order
- 1, 2, 5
- Global polynomial degree
- 2
- Queries outside sampled x range
- 0
Calculation method
Calculation method
Interpolated values in query order
Evaluate the barycentric Lagrange formula using weights 1/product(x_i−x_j); exact node queries return the original ordinate.
Global polynomial degree
Number of distinct samples minus one.
Queries outside sampled x range
Count query coordinates below the smallest or above the largest sample x.
Symbols and units
- a
- Samples: x,y, one pair per line
- b
- Query x values
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- One global interpolating polynomial through 2–25 distinct real nodes. High-degree interpolation and extrapolation can be ill-conditioned; no claim of an underlying physical model is made. Double-precision results are approximate. Numeric tables use 12 significant digits and display components at roundoff scale (32 machine epsilons relative to their row or relevant calculation scale) as zero; scalar diagnostics retain full precision.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
SciPy: Lagrange interpolation ↗
Background reading; this does not imply endorsement or independent review of SumFizz.