More Precise Floating point Data Types than double?

Question

In my project I have to compute division, multiplication, subtraction, addition on a matrix of double elements. The problem is that when the size of matrix incr

Answer 1

You might want to consider the sequence of operations, i.e. do the additions in an ordered sequence starting with the smallest values first. This will increase overall accuracy of the results using the same precision in the mantissa:

1e00 + 1e-16 + ... + 1e-16 (1e16 times) = 1e00
1e-16 + ... + 1e-16 (1e16 times) + 1e00 = 2e00

The point is that adding small numbers to a large number will make them disappear. So the latter approach reduces the numerical error