Graduate Why is Picard Iteration Named Fixed Point Iteration?

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The term "fixed point iteration" refers to a method used in both differential equations and numerical analysis to find fixed points of functions. In the context of Picard iteration, it involves iteratively approximating solutions to differential equations by using previous approximations as inputs. The name derives from the concept that the iteration process converges to a point that remains unchanged by the function applied to it. This method is essential for solving equations where direct solutions are difficult to obtain. Understanding its application in these mathematical contexts clarifies the terminology and its significance.
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picard iteration is also known as fixed point iteration
hi, i want to figure out why it is named as fixed point iteration.
 
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