User:Lmb.ohio

Example of Evaluating a Function
Let f(x) = 2x - 3 What is f(1)? Solution: Step 1 - Substitute 1 for x in f(x): f(1) = 2(1) - 3

Step 2 - Simplify: f(1) = 2-3; therefore, f(1) = -1

Quiz: Evaluating a Function
{Let g(t) = 3t+5. Evaluate g(2). + g(2) = 11. - g(2) = 10. - g(2) = 9. - g(2) = 8.
 * type=""}

{Let g(t) = 3t+5. Evaluate g(t-2). - g(t-2) = 3t+4. + g(t-2) = 3t-1. - g(t-2) = 3t-6 - g(t-2) = 3t+2
 * type=""}

{Let g(t) = 3t+5. Evaluate g(t) - g(2). - g(t-2) = 3t+4. - g(t-2) = 3t-1. + g(t-2) = 3t-6 - g(t-2) = 3t+2
 * type=""}

Wikiversity Page Edit
For homework #7, problem number 1, I edited the Topic:Numerical analysis/Newton form exercise page. This page had one example of how to use the Newton Polynomial. The solution that was already on the page skipped many steps; therefore, I edited the solution to make it more complete. I also added another exercise to this page on how to interpolate a polynomial using the Newton polynomial when a new point is added.

Final Project
For my final project I plan to make a wikiversity page on Neville's Algoithm. I plan to include sample code, examples, as well as a quiz.
 * A bit vague but okay. Make the sample code something people will learn from rather than copy. Avoid overlapping with Topic:Numerical analysis/Newton form example, Topic:Numerical analysis/Newton form exercise, or User:La740411ohio. Mjmohio (talk) 16:18, 7 November 2012 (UTC)

Project Report for User:Lmb.ohio
For Introduction to Numerical Analysis, Fall 2012.

Introduction
My final project is about Neville's Algorithm.The topic of Neville's Algorithm is important because it allows you to evaluate a function at a certain value without actually finding the coefficients of the polynomial. It is difficult to understand using only Wikipedia because there are no examples given. Wikipedia basically gives the definition of Neville's Algorithm, but does not go into any detail how you apply it or how to write a Matlab code.

To facilitate learning of this topic, I created examples illustrating how to use Neville's Algorithm, an exercise to further develop skills at applying Neville's Algorithm, sample code showing how to begin the Matlab code of Neville's Algorithm, and a quiz about Neville's Algorithm to reinforce the ideas on both the Wikipedia Neville's Algorithm page and the Wikiversity Neville's Algorithm examples page.

Contribution
I created an example illustrating how to evaluate the function $$\frac{1}{\sqrt{x}}$$ at $$81$$. I chose this particular example because it is a good illustration that Neville's Algorithm can produce a fairly accurate approximation of a function at a particular value.

I created a second example that looked at the example given on the  Newton Form exercises page on Wikiversity and evaluated the function at $$f(x)$$ at $$3$$ using Neville's Algorithm. I choose this example to show that by using Neville's Algorithm to evaluate a function at a particular point, you can skip the steps used the Newton form to find the coefficients.

I also created an exercise to allow the reader to develop their skills at applying Neville's Algorithm. I choose this particular example to illustrate how Neville's Algorithm applies to a higher degree polynomial.

I created sample code showing the basic outline of Matlab code used to evaluate an interpolating polynomial using Neville's Algorithm. The code gives the inputs and output that are needed as well as the basic steps of the code, but leaves some blanks throughout the code as questions for the reader at the end of the code.

Finally, I created a quiz about when you use Neville's Algorithm, the formula of Neville's Algotithm, as well as a practice question using Neville's Algorithm. These questions reinforce the ideas presented on the Wikipedia page as well as on the Wikiversity exercises page. I choose these three particular questions, because they illustrate the three of the most important ideas of Neville's Algorithm.

Future Work
In the future, it would be beneficial if some proofs were added to Wikiversity about Neville's Algorithm, such as why Neville's Algorithm always works. More work could also be completed on the convergence of Neville's Algorithm.

Conclusions
In this project I added examples, an exercise, a quiz, and a Matlab code with questions to Wikiversity on the topic of Neville's Algorithm. I think this is a valuable contribution because the Wikipedia page on Neville's Algorithm did not go into much detail on the topic. This page gave the formula and a basic idea, but did not give any detail on how to apply the method. Overall, I think the Wikiversity pages I added on Neville's Algorithm will be beneficial to someone who is studying polynomial interpolation for the first time.