Direktni metodi računaju rešenja problema u konačnom broju koraka. These methods would give the precise answer if they were performed in [[Computer numbering formats|infinite precision arithmetic]]. Examples include [[Gaussian elimination]], the [[QR algorithm|QR]] factorization method for solving [[system of linear equations|systems
of linear equations]], and the [[simplex method]] of [[linear programming]]. In practice, [[Floating point|finite precision]] is used and the result is an approximation of the true solution (assuming [[Numerically stable|stability]]).
In contrast to direct methods, [[iterative method]]s are not expected to terminate in a finite number of steps. Starting from an initial guess, iterative methods form successive approximations that [[Limit of a sequence|converge]] to the exact solution only in the limit. A convergence test, often involving [[Residual (numerical analysis)|the residual]], is specified in order to decide when a sufficiently accurate solution has (hopefully) been found. Even using infinite precision arithmetic these methods would not reach the solution within a finite number of steps (in general). Examples include [[Newton's method]], the [[bisection method]], and [[Jacobi iteration]]. In computational matrix algebra, iterative methods are generally needed for large problems.
Iterative methods are more common than direct methods in numerical analysis. Some methods are direct in principle but are usually used as though they were not, e.g. [[GMRES]] and the [[conjugate gradient method]]. For these methods the number of steps needed to obtain the exact solution is so large that an approximation is accepted in the same manner as for an iterative method.
=== Diskretizacija ===