Fixed-Point Iteration Calculator
Iterate a fixed-point formula and track convergence.
Calculator
What this calculator teaches
Iterate a fixed-point formula and track convergence.
This calculator focuses on numerical methods with a result, formula context, and step-by-step interpretation so the page is more useful for students than a bare answer.
Formula & Symbols
| Concept | Formula | Meaning |
|---|---|---|
| Fixed point | x = g(x) | A solution is a value unchanged by g. |
| Babylonian update | g(x)=0.5(x+N/x) | A fixed-point formula for square roots. |
Step-by-Step Example
- Start with a guess.
- Apply xₙ₊₁=0.5(xₙ+N/xₙ).
- Watch the values converge.
Where students use this
Common Mistakes to Avoid
Check conditions such as convergence, step size, valid units, matrix dimensions, or stable iteration before using the answer.
Keep extra digits during intermediate work and round only the final result.
The result is useful only when you understand what the formula, units, and restrictions mean.
Frequently Asked Questions
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Formula Explorer connections
Interpretation: This relationship converts, summarizes or checks numerical quantities using standard arithmetic and measurement rules. Assumption: Use consistent units, preserve enough significant digits, and round only the final result unless the method states otherwise.