Numerical Analysis Questions & Answers  


I'm not sure what you mean and I can't find 6b. Please formulate your question better.






In this case, you have to find the order of convergence using the results obtained in (a). That is, don't derive an analytical expression for $p$, but find $p$ from the results. Hint: $p$ may change as the solution progresses towards the root. You can find the root (needed to evaluate the error) through the results as well. Good question: 2 points bonus.




Well, solving a system of equations with the secant method is not so different to solving a single equation. When solving a single equation, the derivative $f^\prime$ is replaced by a firstorder approximation. Do the same here and use very small $\Delta x$ and $\Delta y$ for the first iteration. 1 point bonus.




You're not doing anything wrong. If you would answer this in the exam, you would get full points. But, in general, we do not know what the exact root is. Thus, it is necessary to approximate it as the solution at the next iteration. If using the solution at the next iteration (i.e. 4.573738E+00) as the root, you'll get the answer listed. I made this more clear within the question formulation. 2 points bonus.




I don't understand well your question. Why are there only 3 terms within $p_3(x)$ and not 4? Also, the rest of the question doesn't make much sense to me. You need to explain this better. 0.5 point bonus for the effort. Make sure to use the PREVIEW button and check if the question looks as intended. Also, use \$\$ and not \$ for long math expressions.




Good question. We need to find $b_N$ because $a_{N1}$ and $c_{N1}$ depend on $b_N$. So, we only need to find $N1$ intervals, but we need to find $N$ bs. 2 points bonus.




Hm, I'm not sure what confuses you. Answers to your questions were given in class.




There's little work involved when moving numbers around in memory compared with additions or multiplications. Hence why it's not counted. 1 point bonus.




You can find the exact value by using a very large $N$. So, just double $N$ until the value of the integral doesn't change significantly anymore and use this as the exact value. 2 points bonus.




No, there is no work done when doing the pivoting operation because there is no addition or multiplication. This was mentioned above for a similar question.




That's for you to find out. Check if you obtain reasonable convergence rates using your approach when $N$ is small (i.e. as you would expect for the Simpson rule) and if so, it means it's fine.




Hm, didn't I mention this in class..? It's a good observation, but not a question.



$\pi$ 