Numerical Analysis

The metadata subpage is missing. You can start it via filling in this form or by following the instructions that come up after clicking on the [show] link to the right.

Do you see this on PREVIEW? then SAVE! before following a link. To find out more about the use of metadata for the management of Citizendium pages, see CZ:Metadata. You may see this box for one of two reasons. Either: A - New page has been created, or subpages template was added to an existing page B - Cluster move is in progress Click either the A or B link for further instructions. [Feel free to recommend improvements to the text or links in this template] A - For a New Cluster use the following directions Subpages format requires a metadata page. Using the following instructions will complete the process of creating this article's subpages. Click the blue "metadata template" link below to create the page. On the edit page that appears paste in the article's title across from "pagename =". You might also fill out the checklist part of the form. Ignore the rest. For background, see Using the Subpages template Don't worry--you'll get the hang of it right away. Remember to hit Save! the "metadata template". However, you can create articles without subpages. Just delete the {{subpages}} template from the top of this page and this prompt will disappear. :) Don't feel obligated to use subpages, it's more important that you write sentences, which you can always do without writing fancy code. [Feel free to recommend improvements to the text or links in this template] B - For a Cluster Move use the following directions The metadata template should be moved to the new name as the first step. Please revert this move and start by using the Move Cluster link at the top left of the talk page. The name prior to this move can be found at the following link. [Feel free to recommend improvements to the text or links in this template]

---

Numerical analysis is the study of finding or approximating the solution to a mathematical problem using a computer. Differential equations and linear algebra are two of the largest fields of study within this area.

Accuracy and Error

Errors will be introduced whenever computers are asked to do calculations involving real numbers, since a computer can only store a real number up to a finite number of significant figures. These errors can be multiplied over the course of many calculations.

Some algorithms produce more errors than others. For example, suppose we want to calculate 2,000,001 + 1/3 - 2,000,000. For the purposes of this example, we will work in the usual base ten rather than in binary, and we will suppose that we are accurate to only eight significant figures. Now, how shall we do this calculation? First of all, we must do the division to find that 1/3 = 0.33333333 (to eight significant figures). Suppose that we next choose to add 2,000,001 and 0.33333333 to get 2,000,001.3 (again, to eight significant figures). Now we subtract 2,000,000 to get 1.3000000. This answer is accurate to only two significant figures! On the other hand, if the algorithm was somehow set up to subtract the 2,000,000 before adding 0.33333333, the final answer would still be accurate to eight significant figures. Thus, algorithms are often constructed so as to try to avoid adding numbers of wildly different magnitude.