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
Dimensions - matrix: The size and length functions in the MATLAB are used to find array dimensions. Length function returns the number of elements in the vector. The size func

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

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, >>

fprintf function - File function: The fprintf function really returns the number of bytes which was written to the file, therefore if you do not want to see that number, suppr

Illustration of Logical vectors: Calling the function appears to return similar vector as simply vec > 5, and summing the result still works to determine how many elements wer

Writing and Reading Spreadsheet Files: The MATLAB functions xlswrite & xlsread will write to and read from the spreadsheet files which have the extension .xls. For illustratio

sprintf function: The sprintf function works precisely like the fprintf function, but rather than printing it generates a string. Here are some illustrations in which the outp

Strings as matrix: The matrix can be generated, that consists of strings in each row. Therefore, essentially it is created as a column vector of strings, but the final result

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

Using Functions with the Vectors and Matrices: As MATLAB is written to work with the vectors and matrices, the whole vector or matrix can be passed as an argument to the funct