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An iterative method is called convergent if the corresponding sequence converges for given initial approximations. A mathematically rigorous convergence analysis of an iterative method is usually performed; however, heuristic-based iterative methods are also common.
In numerical mathematics, relaxation methods are iterative methods for solving systems of equations, including nonlinear systems. [ 1 ] Relaxation methods were developed for solving large sparse linear systems , which arose as finite-difference discretizations of differential equations .
In numerical analysis, fixed-point iteration is a method of computing fixed points of a function.. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is + = (), =,,, … which gives rise to the sequence,,, … of iterated function applications , (), (()), … which is hoped to converge to a point .
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 ...
In practical numerical computations, asymptotic rates and orders of convergence follow two common conventions for two types of sequences: the first for sequences of iterations of an iterative numerical method and the second for sequences of successively more accurate numerical discretizations of a target.
In numerical analysis, Steffensen's method is an iterative method for numerical root-finding named after Johan Frederik Steffensen that is similar to the secant method and to Newton's method.
In numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges.
Wood–Armer method — structural analysis method based on finite elements used to design reinforcement for concrete slabs; Isogeometric analysis — integrates finite elements into conventional NURBS-based CAD design tools; Loubignac iteration; Stiffness matrix — finite-dimensional analogue of differential operator; Combination with ...