I was studying Numerical Analysis by K. Mukherjee; there he discussed Loss of Significant Figures by Subtraction, as followed:
In the subtraction of two approximate numbers, a serious type of error may be present when the numbers are nearly equal. ...
He showed how the number of significant figures got decreased after subtraction.
In order to dig more, I googled and came across the term catastrophic cancellation.
I did try to read the wiki article but it was full of terms especially floating point arithmetic which I am really not acquainted it; I did try to read the latter's wiki article but couldn't comprehend the definition:
The term floating point refers to the fact that a number's radix point (decimal point, or, more commonly in computers, binary point) can "float"; that is, it can be placed anywhere relative to the significant digits of the number.
Radix point can float? Unfortunately, I failed to visualise that.
However, my main question, even if there is an error due to the loss of the significant figures, why is this error "catastrophic"?
I found in a decade old page that
The relative error here is infinite.
But how could the loss of significant figures led to an infinite magnitude of relative error?
Could anyone please explain the reason behind the term "catastrophic" keeping in mind that I'm not acquainted with floating point arithmetic?