Assuming we have a specific equation involving two coefficients A and B.
If A is given and B is unknown, B can be numerically and uniquely obtained by performing root-finding on the above equation(process X hereafter).
If B is given and A is unknown, A can be analytically and uniquely obtained by the same equation(process Y hereafter).
The scenario I concerned:
If A is given arbitrarily, then B can be numerically obtained from A by root-finder. Afterwards, we can transform B into A' by process Y. Although A is theoretically equal to A', there is always a machine epsilon between original A and A' because no computer has infinite precision floating point number - in other words, if we had infinite precision floating point number on computer, then A would be exactly equal to A'.
Now, My question is how do I fluently rewrite the above scenario in the following pattern:
[The error between A and A'...]
[The error of A between ... and ...]
The sentence I have tried to write is as follows:
- The figure shows the error of A between the given and calculated values from B, which is computed through root-finder.
- The figure shows the error between given A and A calculated from B, which is computed through root-finder.
Is there still room for improvement? I will be grateful for any help you can provide.
To Jason Bassford: Both X and Y processes are actually carried out on computer. This is a major cause of why there is an error between A and A'.(the magnitude of error depend heavily on numerical precision)