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
Print an imaginary number: To print an imaginary number, the function disp will show both parts automatically: >> disp(z1)    4.0000 + 2.0000i The function fprint

Counting in a While Loop: Whenever it is not known ahead of the time how many values will be entered into the script, it is often essential to count the number of values which

Illustration of Minimum and Maximum Value Both of these functions also return the index of the minimum or maximum value; when there is more than one occurrence, it returns the

Concatenation: The String concatenation means to join the strings altogether. Of course, as strings are merely vectors of the characters, the technique of concatenating vector

Built-in function for Differentiation: The MATLAB has a built-in function, diff that returns the differences between consecutive elements in a vector. For illustration, >>

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 co

Fliplr function: The fliplr function "flips" the matrix from left to right (in another words the left-most column, the first column, become the last column and so on), and the

Function fopen - file function: The permission string in the call to the fopen function identifies that the file is opened for writing to it. Just as when reading from a file,

strvcat function - concatenation: The function strvcat will concatenate it vertically, that means that it will generate a column vector of the strings.   >> strvcat(fir