Types of Errors in Numerical Analysis
- The abacus: an early math calculatorold math game image by peter Hires Images from Fotolia.com
In the world of math, the practice of numerical analysis is well known for focusing on algorithms as they are used to solve issues in continuous math. The practice is familiar territory for engineers and those who work with physical science, but it is beginning to expand further into liberal arts areas as well. This can be seen in astrology, stock portfolio analysis, data analysis and medicine. Part of the application of numerical analysis involves the use of errors. Specific errors are sought out and applied to arrive at mathematical conclusions. - The round-off error is used because it a representation of every number as a real number is not possible. So rounding is introduced adjust for this situation. A round-off error, represents the numerical amount between what a figure actually is versus its closest real number value, depending on how the round is applied. For instance, rounding to the nearest whole number means you round up or down to what is the closest whole figure. So if your result is 3.31 then you would round to 3. Rounding the highest amount would be a bit different. In this approach, if your figure is 3.31, your rounding would be to 4. In terms of numerical analysis the round-off error is an attempt to identify what the rounding distance is when it comes up in algorithms. It's also known as a quantization error.
- A truncation error occurs when approximation is involved in numerical analysis. The error factor is related to how much the approximate value is a variance from the actual value in a formula or math result. For example, take the formula of 3 times 3 plus 4. The calculation equals 28. Now, break it down and the root is close to 1.99. The truncation error value is equal to 0.01.
- As a type of truncation error, the discretization error focuses on how much a discrete math problem is not consistent with a continuous math problem.
- If an error stays at one point in an algorithm and doesn't aggregate further as the calculation continues, then it is considered a numerically stable error. This happens when the error causes only a very small variation in the formula result. If the opposite occurs, and the error propagates bigger as the calculation continues, then it is considered numerically unstable.
- Math errors, unlike the inference of their name, come in useful in statistics, computer programming, advanced mathematics and much more. The error evaluation provides significantly useful information, especially when probability is required.
