Question by Student 201427129 professor i wonder about Q#2 for Q#4-2 to solve Q#4, i must find interactions of Q#2 by secant method. when i try, it give only condition $x_0$ accroding to lecture book, that method have 2 conditions so i guess $x_1$ by orders of convergence to yield the at least itercations(bisection problems are solved in #Q1 with same way$\epsilon_{n+1}=\frac{1}{2}\epsilon_n\;\; \epsilon_k=\frac{\pi}{2^k}\;\; 3.142-\pi=\frac{\pi}{2^k}$ ) but in #Q2 problem is too hard because it's convergence is superliner. ($k ^{p} = \frac{1} {2} *|\frac{sin(\pi)}{cos(\pi)}|=0, \epsilon =0,x_{n+1}=root)$ it means that $x_{n+1}=cost?!?!?$ so confused.. so i can't find proper and the smallest interactions can you give some ways?
You should not determine $k$ or $p$ analytically from the function here. Rather you should find them from the error obtained at each iteration only.
There's some problems in your question formulation: you need to make sure the math is surrounded by \$signs. Please post again below with correct typesetting.  Question by Student 201529190 Dear Professor，for the work times of diagonal matrix. To turn the number to zero from bottom. At$row_{N}$no work so,$work_{N=0}=o$. At$row_{N-1}$,we need turn$A_{N-1,N}$to 0. It use 4 works (2moct+2add).so,$ work_{N-1}=4$\begin{bmatrix} .. &.. & .. & .. & ..\\ ..& ..& ..&.. &.. \\ ..& .. & .. &.. &.. \\ ..& .. & A_{N-1,N-1} & A_{N-1,N} &X_{N-1} \\ ..& ..& .. & A_{N,N} & X_{N} \end{bmatrix} At$row_{N-2}$, we need turn$A_{N-2,N-1}$and$A_{N-2,N}$to 0. It use 8 works 2*(2moct+2add).so$ work_{N-2}=8$\begin{bmatrix} .. &.. & .. & .. & ..\\ ..& ..& ..&.. &.. \\ ..&A_{N-2,N-2}& A_{N-2,N-1} &A_{N-2,N} &X_{N-2} \\ ..& .. & A_{N-1,N-1} & 0 &X_{N-1} \\ ..& ..& .. & A_{N,N} & X_{N} \end{bmatrix} then \begin{bmatrix} .. &.. & .. & .. & ..\\ ..& ..& ..&.. &.. \\ ..&A_{N-2,N-2}& 0 &0 &X_{N-2} \\ ..& .. & A_{N-1,N-1} & 0 &X_{N-1} \\ ..& ..& .. & A_{N,N} & X_{N} \end{bmatrix} so$ work_{N-3}=12$,$ work_{N-n}=4n$total work$ =\sum_{m=1}^{N-1} 4\times (N-n) =2*(N-1)^{2}\propto N^{2}$. then C2 = 2 This is a very good explanation. There is only a small problem with it: you should have written$B$instead of$X$within the last column. 3 points bonus boost.  Question by Student 201700278 Dear Professor, For Question 1 in Assignment 3, may I know is Gaussian decomposition means Gaussian elimination? I tried to search it online but the results are mostly showing either Gaussian Elimination or LU decomposition. I am confused which method should we use in that question?  10.28.17 Fixed. Good observation. 1 point bonus boost.  Previous 1 ... 8 , 9 , 10 ... 14 Next • Make PDF $\pi\$