If there is an underflow where $0.0000000001$ is considered as $0$. This result has a totally different result with the theoretical calculation.Īnother example is when we want to calculate a division, for example, $x=1/0.0000000001$. However, in the real implementation, for example due to incorrect data type selection, a digital computer will consider the calculation as $100000000000 \times 0=0$.
For example, if we want to calculate $x=100000000000 \times 0.0000000001$, theoretically, the results should be $10$. This situation has a significant implication to computation results. This error occurs when a number close to zero is considered as zero. This error is difficult to find, and sometimes, to resolve as well. These two errors very often cause many numerical computational algorithm that are theoretically correct, but do not give correct or the same results from computation after implementations. There are two types of approximation errors: overflow and underflow errors. Because, the error will be accumulated along the length of the computation chain and computation complexity. This error is called approximation error.Īpproximation error has an important role in intensive numerical computation with digital computers. This representation is the fundamental computing error by using digital computers. One of fundamental aspects in computation with digital computers is to represent a real infinite number with finite number with bits (that have values either 0 or 1).įor example, a real number of $\phi=3.141592653589793… $ needs to be represented in term of finite bits. By knowing these errors, we can at least reduce, or even prevent, the possibility to replicate these errors in our computational tasks.
These errors are usually difficult to find as they are not obvious. In addition, other important aspects in numerical computation, which are, processing speed and numerical optimisation are also discussed. The errors are data overflow and underflow, rounding error, poor conditioning, memory leak. In this post, at least six numerical computation errors are presented. Hence, calculating functions or implementing numerical algorithms in digital computers have limitations. However, our digital computers only process finite binary bits. Commonly, numbers involved in our computation are infinite real numbers.However, digital computers operate as a discrete system. Very often, mathematical functions to compute are continuous.There are at least two inherent problems in numerical computation using digital computers: In numerical computation, many unexpected results occur due to errors related to digital computation instead of errors due to logic or model or formula errors. In many modern science and engineering fields, numerical computation has an essential role to perform meaningful analyses.
0 kommentar(er)
