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Use case: Solving system of linear equations. Example: Determining variables in

Use case: Finding better approximations of the roots of real-valued functions. Example: Refining the zero of $x^2 - 2$ starting with a guess of 1.

Use case: Finding the local minimum of differentiable functions, common in machine learning. Example: Minimizing cost functions like Mean Squared Error in linear regression.

Use case: Solving linear optimization problems in operations research. Example: Maximizing profit $P = 40x + 30y$ subject to constraints.

Use case: Evaluating the impact of risk and uncertainty in prediction and forecasting models. Example: Estimating the value of $\\(\pi\\)$ by simulating random points in a square and counting those in a quarter circle.

Use case: Signal processing to decompose a function into its constituent frequencies. Example: Filtering noise from a signal by transforming, modifying, and performing an inverse transform.