Examples
Examples
Try the starting example
- Restricted expression f(x)
- x - 2
- Derivative expression, or auto
- auto
- Initial guess
- 0
- Absolute residual tolerance
- 1e-10
- Maximum iterations
- 20
- Final iterate
- 2
- Function value at final iterate
- 0
- Newton updates used
- 1
- Iteration status
- Converged by residual
- Trace: x, f(x)
- 0, -2; 2, 0
Try another scenario
- Restricted expression f(x)
- x^2 - 4
- Derivative expression, or auto
- auto
- Initial guess
- 3
- Absolute residual tolerance
- 1e-10
- Maximum iterations
- 1
- Final iterate
- 2.166667
- Function value at final iterate
- 0.694444
- Newton updates used
- 1
- Iteration status
- Iteration limit reached
- Trace: x, f(x)
- 3, 5; 2.16666666667, 0.694444444444
Calculation method
Calculation method
Final iterate
Update x←x−f(x)/f′(x), using the supplied restricted derivative or a symbolic derivative of the validated expression.
Function value at final iterate
Evaluate f at the final iterate.
Newton updates used
Count completed updates; the initial observation is not an update.
Iteration status
Convergence requires the absolute residual tolerance; report iteration limit, zero-derivative error or stagnation honestly.
Trace: x, f(x)
Show the initial and every subsequent x/f(x) pair.
Symbols and units
- a
- Restricted expression f(x)
- b
- Derivative expression, or auto
- c
- Initial guess
- d
- Absolute residual tolerance
- e
- Maximum iterations
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
- Scalar Newton iteration with at most 100 updates. Convergence is not guaranteed, and a supplied derivative is your responsibility. Zero derivatives, undefined evaluations and stagnation are explicit failures. Restricted expressions allow x (and y for ODEs), pi, e, + - * / ^, and sin, cos, tan, sec, csc, cot, exp, log, sqrt, abs, sinh, cosh, tanh, sech, csch, coth. Trigonometric arguments are in radians. 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: Newton root iteration ↗
Background reading; this does not imply endorsement or independent review of SumFizz.