Iterative method - Revision history

Karl Jones: /* See also */

2016-10-13T11:42:44Z

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2016-10-13T02:36:42Z

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2016-08-25T02:59:46Z

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‎External links

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Karl Jones: Created page with "In computational mathematics, an '''iterative method''' is a mathematical procedure that generates a sequence of improving approximate solutions for a class of problems...."

2016-08-25T02:52:57Z

Created page with "In computational mathematics, an '''iterative method''' is a mathematical procedure that generates a sequence of improving approximate solutions for a class of problems...."

New page

In [[computational mathematics]], an '''iterative method''' is a mathematical procedure that generates a sequence of improving approximate solutions for a class of problems.

== Description ==

A specific implementation of an iterative method, including the termination criteria, is an [[algorithm]] of the iterative method.

An iterative method is called convergent if the corresponding sequence converges for given initial [[Approximation|approximations]].

A mathematically rigorous convergence analysis of an iterative method is usually performed; however, [[heuristic]]-based iterative methods are also common.

In the problems of [[Root-finding algorithm|finding the root]] of an equation (or a solution of a system of equations), an iterative method uses an initial guess to generate successive [[Approximation|approximations]] to a solution.

In contrast, direct methods attempt to solve the problem by a finite sequence of operations. In the absence of [[Rounding error|rounding errors]], direct methods would deliver an exact solution.

Iterative methods are often the only choice for [[Nonlinear equation|nonlinear equations]].

However, iterative methods are often useful even for [[Linear equation|linear problems]] involving a large number of [[Variable (mathematics)|variables]] (sometimes of the order of millions), where direct methods would be prohibitively expensive (and in some cases impossible) even with the best available [[Computing performance|computing power]].

== See also ==

* [[nth root algorithm]]
* [[Broyden's method]]
* [[Cryptographically secure pseudorandom number generator]] — a class of functions designed specifically to be unsolvable by root-finding algorithms.
* [[GNU Scientific Library]]
* [[Graeffe's method]]
* [[MPSolve]]
* [[Multiplicity (mathematics)]]
* [[Polynomial greatest common divisor]]
* [[Polynomial]]
* [[Root-finding algorithm]]
* [[System of polynomial equations]] — root-finding algorithms in the multivariate case

== External links ==

* [https://en.wikipedia.org/wiki/Root-finding_algorithm Root-finding algorithm] @ Wikipedia

[[Category:Mathematics]]

@@ Line 20: / Line 20: @@
 * [[Gradient descent]]
 * [[Matrix splitting]]
 * [[Root-finding algorithm]]

← Older revision		Revision as of 02:58, 25 August 2016
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	== See also ==		== See also ==
−
−	* [[nth root algorithm]]
−	* [[Broyden's method]]
−	* [[Cryptographically secure pseudorandom number generator]] — a class of functions designed specifically to be unsolvable by root-finding algorithms.
−	* [[GNU Scientific Library]]
−	* [[Graeffe's method]]
−	* [[MPSolve]]
−	* [[Multiplicity (mathematics)]]
−	* [[Polynomial greatest common divisor]]
−	* [[Polynomial]]
−	* [[Root-finding algorithm]]
−	* [[System of polynomial equations]] — root-finding algorithms in the multivariate case

	== External links ==		== External links ==

← Older revision		Revision as of 02:55, 25 August 2016
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	* [https://en.wikipedia.org/wiki/Iterative_method Iterative method] @ Wikipedia		* [https://en.wikipedia.org/wiki/Iterative_method Iterative method] @ Wikipedia

		+
		+	[[Category:Computer science]]
		+	[[Category:Computing]]
	[[Category:Mathematics]]		[[Category:Mathematics]]

← Older revision		Revision as of 02:59, 25 August 2016
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	== See also ==		== See also ==
		+
		+	* [[Matrix splitting]]
		+	* [[Root-finding algorithm]]

	== External links ==		== External links ==

@@ Line 33: / Line 33: @@
 == External links ==
-* [https://en.wikipedia.org/wiki/Root-finding_algorithm Root-finding algorithm] @ Wikipedia
+* [https://en.wikipedia.org/wiki/Iterative_method Iterative method] @ Wikipedia
 [[Category:Mathematics]]