How can I increase the precision if I have around 45,000.

In an multinomial expansion I have 45,000 terms to add. The result should be less than 1. However due to addition of so many terms the error also gets magnified; and gives random deviations of significant values in the result. Using double() doesn't help either.

[Jan]

Using "double()" instead of what? Please describe the input data more explicitly.

[Arnav Mohan]

I mean instead of calculating F=f(x)+g(x); I use F=double(f(x))+ double(g(x))

Answer 1

[Jan]

I'm not sure if I understand the problem correctly: You calculate the summ and suffer from the limited accuracy? This would be one effect of the nature of the sum, which is numerical instable. As workaround you can increase the precision to 128 or 196 bit floating point accumulation using the "Knuth" methods in: FEX: XSum.

[Arnav Mohan]

Yes; that's right, i suffer from a limited accuracy. for so many terms even if I write a multinomial series which should result in 0; I was getting around 10000. whereas for lower number of terms I get the right answer which is 0.

And do you have the matlab code for XSum also?

Answer 2

[Arnav Mohan]

Yes; that's right, i suffer from a limited accuracy. for so many terms even if I write a multinomial series which should result in 0; I was getting around 10000. whereas for lower number of terms I get the right answer which is 0.