briefly explain why the truncation error tends to decrease as the roundoff error increases (or vice versa). in matlab

The truncation error in numerical analysis refers to the error that occurs due to approximating a mathematical function or operation using a finite number of terms or iterations. On the other hand, roundoff error is the error that occurs due to the limited precision of the computer representation of numbers.

In MATLAB, as the roundoff error increases, the truncation error tends to decrease. This is because the roundoff error affects each individual computation step, while the truncation error is only affected by the overall accuracy of the approximation.

When roundoff error increases, it introduces small errors in the intermediate results of the computations. These errors can cancel out or reduce the impact of the truncation error. As a result, the overall error in the final result tends to be smaller.

However, it is worth noting that while increasing the roundoff error may reduce the truncation error, it also introduces additional source of error which can accumulate over multiple computations. Therefore, it is important to strike a balance between the two errors to achieve accurate and reliable results in numerical computations.