extrapolation.en.md

Extrapolation

Extrapolation is used to estimate the limit of a numerical sequence or to predict its trend.

Quick Workflow

1. Input data: paste a multi-column table or upload a text file
2. Choose an extrapolation method (see below)
3. Set options:
   • Reference column: used to estimate the uncertainty
   • Max-diff column: automatically choose the reference column with the largest deviation from the extrapolated value (more conservative)
   • Multi-precision mp.dps: numerical precision
   • Result uncertainty significant digits
4. Run: click “Run Extrapolation & Generate LaTeX”

Methods

Power-law extrapolation (3-point)

Suitable for sequences of the form f(x) = A*x^(-p) + C.

Parameters:

• x1, x2, x3: x coordinates of the three points
• power_exponent: fixed power exponent p (optional)
• power_seed: initial guess for p

Use cases: basis-set extrapolation in quantum chemistry, precision extrapolation for numerical integration, etc.

Richardson extrapolation

Suitable for asymptotic expansion sequences.

Use cases: numerical differentiation/integration, finite-difference methods.

Shanks transform / Wynn ε algorithm

General-purpose sequence acceleration.

Use cases: series summation, accelerating iterative methods.

Levin u-transform

Specialized for oscillating or alternating series.

Parameters:

• levin_variant: Levin variant (default 'u')

Custom formula

Use a custom mathematical formula for extrapolation.

Formula syntax:

• Use A, B, C or column names to reference data columns
• Use x1, x2, x3 as column aliases by order
• Supported functions/constants: same whitelist as error propagation and custom fit models (use the in-app “Formula Help” as the source of truth; see the Theory page for the full list)
• Example: (C - B)^2/(B - A) + C