While running this matlab code the value of x(513) is infinite value.But while calculating manually it is a finite value only.

x(1)=3.58;
for i=2:(513)
    x(i)=4*(x(i-1));
end

Why this kind of error is happening in matlab?

Answer 1

[Stephen23]

Because your calculation exceeds the largest value that can be represented using the floating point class double:

 >> realmax()
 ans =   1.7977e+308

and values larger than that are represented as Inf. The second-to-last value is 1.6089e+308 which you then multiply by four to get Inf. There is no surprise there, this is the expected behavior.

Note also that you can easily generate this vector more efficiently without a loop:

 cumprod([3.58,4*ones(1,512)])

All beginners need to learn what floating point numbers are and how to work with them, otherwise their numeric calculations can easily turn into meaningless rubbish. For a readable introduction to floating point arithmetic, look at Cleve's Corner article from 1996: Floating Points.

For more rigorous and detailed information on floating point arithmetic, read the following paper: What Every Computer Scientist Should Know About Floating Point Arithmetic.