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Fixed-Point Contraction Error Bound

Bound remaining iteration error from a contraction factor and successive iterate difference.

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FormulaError Bound = q*delta/(1-q); Additional Iterations = max(0,ceil(log(target*(1-q)/(q*delta))/log(q)))
Sources and model references

Made for real tasks

  • Bound remaining iteration error from a contraction factor and successive iterate difference.
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Worked example

Inputs

Contraction factor
0.5 ratio
Latest iterate difference
0.01 number
Target error
0.0001 number

Expected results

Error Bound
0.01 number
Additional Iterations
7 iterations

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 contraction factor, latest iterate difference, target error.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "q": 0.5,
  "delta": 0.01,
  "target": 0.0001
}

Accuracy and scope

Only valid when q is a proven Lipschitz contraction bound over the relevant invariant domain.

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.