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The Golden Section Search (GSS) is a numerical optimization technique used to find the minimum (or maximum) of a unimodal function without requiring derivatives. It uses the golden ratio (φ ≈ 1.618) to efficiently narrow down the search interval, making it particularly useful when the function is expensive to evaluate or when derivatives are unavailable.

Use GSS when you have a unimodal function (single peak or valley), don't have access to derivatives, or when computing derivatives is computationally expensive. It's ideal for functions that are continuous but not necessarily differentiable. For multimodal functions or when you need faster convergence and have derivatives available, consider methods like Newton-Raphson or gradient descent.

The accuracy depends on your chosen tolerance (ε). Our solver uses double-precision floating-point arithmetic and can achieve accuracy down to machine precision. A typical tolerance of 0.0001 provides 4 decimal places of accuracy, while 0.000001 gives 6 decimal places. The algorithm guarantees convergence to the true minimum within your specified tolerance for unimodal functions.

Yes! Our solver includes a maximization mode. Simply select "Maximization" from the optimization mode dropdown. The algorithm internally negates the function to convert the maximization problem into a minimization problem, then returns the correct maximum value and location.

The solver supports a wide range of mathematical operations including polynomials (x², x³), trigonometric functions (sin, cos, tan), exponentials (e^x), logarithms (log, ln), square roots (√), and fractions. You can combine these with standard arithmetic operators (+, -, *, /, ^). Use the MathQuill input field for intuitive mathematical notation.

Absolutely! All computations are performed entirely in your browser using Pyodide (Python compiled to WebAssembly). No data is sent to any server—your functions, inputs, and results never leave your device. The session history is stored only in your browser's memory and is cleared when you close the tab.