Iteraatiomenetelmä

Iteraatiomenetelmä is a general term in mathematics and computer science referring to a method that repeatedly applies a process to find a solution. Instead of a direct calculation, an iterative method starts with an initial guess and refines it through a series of steps, or iterations, until a satisfactory level of accuracy is reached. Each iteration uses the result from the previous one to produce a better approximation.

These methods are widely used for solving various problems, including finding roots of equations, solving systems of linear equations, and optimizing functions. For example, the Newton-Raphson method is a well-known iterative technique for finding the roots of a function. In numerical analysis, iterative methods are crucial when analytical solutions are difficult or impossible to obtain.

The success of an iterative method depends on factors such as the choice of the initial guess, the convergence properties of the algorithm, and the stopping criteria used to determine when the solution is accurate enough. If an iterative method does not converge, it means the approximations do not approach a meaningful solution. The speed of convergence, how quickly the method approaches the solution, is also an important consideration.