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12 Iteration

# 12 Iteration - 12 Iteration Iteration vs Recursion Any...

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Iteration - 1 12 - Iteration Iteration vs. Recursion Any problem that can be solved recursively can also be solved iteratively . In recursion, you start at the end of a problem and work backward until you get to your base case. With iteration, you start at the base case and work forward. Recursive programs have to have many copies of themselves “open” at a time. Iterative programs do not. They just loop until they reach the solution. So, although it often takes more thought to come up with an iterative program than a recursive one, the iterative solution is often faster and uses less memory. In any case, a good programmer needs to know how to think both ways. As a rule of thumb: a recursive function is a function that calls itself. An iterative function just loops. Iteration In the simplest case iteration is a for loop. Suppose for example, we want to compute the dot product of two row vectors a and b . A MATLAB function to do this is: %dotprod.m %calculates the dot product of two row vectors %E77 reader %07-01 D# function [sum] = dotprod(a, b) sum = 0; for i = 1:length(a) sum = sum + a(i) * b(i); end The inner loop goes through a and b one by one as i takes on the values 1:length(a).

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Iteration - 2 Matrix Multiply
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