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THE FEUTEX TOOLKIT

Aitken Sequence Acceleration

Accelerate a linearly convergent sequence from three successive iterates.

Math workspace● Runs in your browser
01 Your input
02 Your result
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FormulaAccelerated = x0-(x1-x0)**2/(x2-2*x1+x0); Correction = (-((x1-x0)**2))/(x2-2*x1+x0)
Sources and model references

Made for real tasks

  • Accelerate a linearly convergent sequence from three successive iterates.
Explore step-by-step workflows →

Worked example

Inputs

First iterate
1 number
Second iterate
1.5 number
Third iterate
1.75 number

Expected results

Accelerated
2 number
Correction
1 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter first iterate, second iterate, third iterate.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "x0": 1,
  "x1": 1.5,
  "x2": 1.75
}

Accuracy and scope

Can be unstable when the denominator is small; convergence is not guaranteed for arbitrary sequences.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.