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Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and ...
An iterative method with a given iteration matrix is called convergent if the following holds lim k → ∞ C k = 0. {\displaystyle \lim _{k\rightarrow \infty }C^{k}=0.} An important theorem states that for a given iterative method and its iteration matrix C {\displaystyle C} it is convergent if and only if its spectral radius ρ ( C ...
Upon iteration, one may find that there are sets that shrink and converge towards a single point. In such a case, the point that is converged to is known as an attractive fixed point. Conversely, iteration may give the appearance of points diverging away from a single point; this would be the case for an unstable fixed point. [11]
A simplified version of a typical iteration cycle in agile project management. The basic idea behind this method is to develop a system through repeated cycles (iterative) and in smaller portions at a time (incremental), allowing software developers to take advantage of what was learned during development of earlier parts or versions of the system.
The fixed point iteration x n+1 = cos x n with initial value x 1 = −1.. An attracting fixed point of a function f is a fixed point x fix of f with a neighborhood U of "close enough" points around x fix such that for any value of x in U, the fixed-point iteration sequence , (), (()), ((())), … is contained in U and converges to x fix.
Iterative design is a design methodology based on a cyclic process of prototyping, testing, analyzing, and refining a product or process.Based on the results of testing the most recent iteration of a design, changes and refinements are made.
In mathematics, power iteration (also known as the power method) is an eigenvalue algorithm: given a diagonalizable matrix, the algorithm will produce a number , which is the greatest (in absolute value) eigenvalue of , and a nonzero vector , which is a corresponding eigenvector of , that is, =.
Iteration means the act of repeating in the contexts of mathematics, computing and project management, particularly software development. It can also refer to: Iterated function, in mathematics "Iteration", a song from Potemkin City Limits, the fourth full-length album by the punk rock band Propagandhi