The direct method uses a fixed number of steps to find the solution to the problem. These methods include gauss elimination and QR algorithm for solving linear equations, simplex method for solving linear programming and so on. If the infinite precision algorithm is adopted, some problems can be solved accurately. However, some problems have no analytical solutions (such as quintic equations), so they cannot be solved directly. Floating-point numbers will be used in computer operation, and the result can be regarded as an approximation of the exact solution on the premise that the operation mode is stable.

Iterative method is a mathematical process to solve problems by finding a series of approximate solutions from an initial estimate. Different from the direct method, when solving a problem by iterative method, there is no fixed number of steps, only approximate solutions can be obtained, and a series of approximate solutions will converge to the exact solution of the problem. Convergence method will be used to judge whether the approximate solution is convergent or not. Generally speaking, even if arithmetic with infinite precision is used, iterative method can't get the exact solution of the problem in a limited number of times.

In numerical analysis, iterative method will be more commonly used than direct method. Such as Newton method, dichotomy, Jacobian method, generalized minimum residue method (GMRES) and * * * yoke gradient method. In computational matrix algebra, large-scale problems generally need to be solved by iterative method.