What does the term 'iterative method' refer to in problem-solving?

The term 'iterative method' refers to a technique that involves repeated approximation. This approach is commonly used in mathematical problem-solving, particularly in scenarios where a direct solution is difficult to find or impossible to express in a closed form.

In iterative methods, an initial guess is taken, and then this guess is refined through a series of calculations. Each iteration moves the approximation closer to the desired solution. As these approximations are repeated, the method typically converges towards a more accurate answer. This is particularly useful in contexts like numerical analysis, optimization, and solving equations.

Iterations are continued until the difference between successive approximations is smaller than a predetermined tolerance level, meaning that the solution is accurate enough for practical purposes. This process showcases the strength of iterative methods in handling complex problems, where quick convergence can be achieved through systematic refinement.

Other options describe methods that lack the essential characteristic of iteration. The concept of requiring only one calculation doesn’t align with the essence of repeated approximation, nor does simply using algebraic manipulation, which can often result in immediate solutions. Lastly, generating a unique solution doesn't inherently relate to the nature of iterative methods, as these may lead to a range of outcomes depending on the initial conditions and parameters used.