Numerical Analysis Questions & Answers  
Question by Student 201427122
Professor, I think that A newton polynomial of Question #3 is not (B) but (C). And at Question #1 $$y=C_1+C_2\sqrt x+C_3x,$$ I use algorism by Least square - combination of functions. I do like this: $$f_1(x_1)=1, f_2(x_2)=\sqrt x, f_3(x_3)=x.$$If I use algorism by just Least square, Is it same correct algorism?
11.22.17
Yes, this seems OK. You're on the right track. You need to further improve your spelling and orthograph thus.
Question by Student 201529190
Dear professor, in Assignment #6 Question#3 .What mean is "multidimensional piecewise-linear interpolation" ? Is it use "multidimensional interpolation "solving ideas ,but use piecewise-linear method?
11.26.17
Yes exactly!
Question by Student 201529190
Dear professor, in Assignment #6 Question#3 .answer should be -0.9,0.7333. Given answer that the order is reversed
True. It's fixed now. 1 point bonus.
Question by Student 201529193
professor, when we use cubic spline to interpolate n+1 points (x0,y0),(x1,y1),...(xn,yn), we can get n piecewise cubic polynomials for n intervals. However, why should we calculate n+1 b in the matrix?
11.27.17
Because $b$ is needed on the boundary nodes as well as on the inner nodes to close the system. Thus, you need $N$ $b$, not $(N-1=n)$ $b$.
Question by Student 201700278
Dear professor, for the $I_i$ equation discussed in the end of the class today, I think it should be $\frac{\Delta x_i ^{3}}{24}f^{\prime \prime}(x_m)$ instead of $\frac{\Delta x_i ^{3}}{3}f^{\prime \prime}(x_m)$ as you have written in class.
Yes, this is quite possible. You'll need to prove this in the next assignment I think.
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