Golden Section Method Calculator: Find Minimum

Input Parameters

Enter the problem details to start the calculation

Function in LaTeX

The tool supports, among others: \(\sin,\cos,\tan,\cot,\sec,\csc,\ln,\log,\lg,\arcsin,\arccos,\arctan,\sqrt{\phantom{x}}, |x|, \exp(x)\)

Start of the interval \(a\)

End of the interval \(b\)

Accuracy \(\varepsilon\)

Max. iterations

Quick example

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Problem Preview

Check your input before starting the calculation

Current setup

\[ f(x)=(x-2)^2+1,\quad x\in[0,5],\quad \varepsilon=0.0001 \]

Input tips

What to enter: the function \(f(x)\), the interval \([a,b]\), the accuracy \(\varepsilon\), and the maximum number of iterations.

Important: for the method to work correctly, the function should be unimodal on the given interval.

The results are displayed with up to 6 decimal places.

Golden Section Method Calculator: How Does It Work?

A golden section method calculator works in a simple way: you enter a function, set the start and end of the interval, choose the accuracy, and run the calculation. The tool immediately presents the problem in a clear format, so you can check whether the function is written correctly, whether the interval is suitable, and whether you have chosen the right accuracy.

Next, the calculator narrows the interval step by step while searching for the minimum of the function. How does it do this? At each iteration, two inner points are placed inside the interval, the function values at these points are calculated, and then one part of the interval is discarded. As a result, you see not only the final answer but also the full reasoning process behind it.

In the end, you get an approximate minimum point, the function value at that point, an iteration table, and a step-by-step graph. Convenient, isn’t it? This kind of calculator helps you not only find the result quickly but also better understand how the golden section method works in practice.