Example of recursive functions, MATLAB in Mathematics

Example of Recursive functions:

This definition is recursive as a factorial is defined in terms of the other factorial. There are two parts to any recursive definition: the common or inductive case, and the base case. We say that in common the factorial of n is defined as n multiplied by the factorial of (n - 1), but the base case is that the factorial of 1 is 1. The base case stops the recursion.

For illustration,

3! = 3 * 2!

2! = 2 * 1!

          1! = 1

= 2

= 6

The way it works is that 3! is defined in terms of the other factorial, as 3 * 2!. This expression cannot yet be computed, as first we have to find out the value of 2!. Therefore, in trying to compute the expression 3 * 2!, interruption by recursive definition occurs. According to the definition, 2! be 2 * 1!. And again, the expression 2 * 1! cannot yet be computed as first we have to find the value of 1!. According to the definition, 1! be 1. As we now know what 1! is, we can carry on with the expression which was just being computed; now we know that 2 * 1! is 2 * 1, or 2. Therefore, now we can finish the earlier expression which was being computed; now we know that 3 * 2! is 3 * 2, or 6.

This is the approach that recursion always works. By recursion, the expressions are place on hold with interruption of the common case of the recursive definition. This keeps occurring until finally the base case of the recursive definition applies. This at last stops the recursion, and then the expressions which were put on hold are computed in the reverse order. In this situation, first the computationof 2 * 1! was done, and then 3 * 2!.

There should always be a base case to end the recursion, and the base case should be reached at several points. Or else, infinite recursion would occur (theoretically, though MATLAB will stop the recursion ultimately).

Posted Date: 10/22/2012 1:29:26 AM | Location : United States







Related Discussions:- Example of recursive functions, Assignment Help, Ask Question on Example of recursive functions, Get Answer, Expert's Help, Example of recursive functions Discussions

Write discussion on Example of recursive functions
Your posts are moderated
Related Questions
Use of logical vector: Determine how many elements in the vector vec were greater than 5, the sum function can be used on the resulting vector isg: >> sum(isg) ans =

Program of built-in factorial function: Calling this function yields similar result as the built-in factorial function: >> fact(5) ans =   120 >> factorial(

Symbolic Expression The solve function solves an equation and returns the solution(s) as symbolic expressions. The answer can be converted to numbers by using any numeric funct

how can reconstruct just part of an image using imreconstruct?

Illustrations of Variable number of output arguments: In the illustrations shown here, the user should actually know the type of the argument in order to establish how many va

Illustration of Labels and prompts: The program below prompts the user for endpoints (x1, y1) and (x2, y2) of a line segment, and computes the midpoint of the line segment, th

If I have a vector representing the packed storage form of a symmetric matrix, how do I perform a cholesky factorisation on that?

Standard Deviation The standard deviation is the square root of variance: The built-in function in a MATLAB for the standard deviation is known as std; the standard dev

Built in recursive function in MATLAB: We have seen that the built-in function in MATLAB to compute factorials, termed as the factorial and we know how to implement the iterat

Give the formula for a rational function that has a hole at x=7 & vertical asmptote at x=-3/2