Another ordering for this matrix K colors the meshpoints alternately red and black. This

Chapter 9, Problem 16

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Another ordering for this matrix K colors the meshpoints alternately red and black. This permutation P changes the normal I, ... ,10 to 1,3,5,7,9,2,4,6,8,10: Red-black ordering P K P T = [~~ ;; ]. Find the matrix D. So many interesting experiments are possible. If you send good ideas they can go on the linear algebra website math.mit.edu/linearalgebra. I also recommend learning the command B = sparse(A), after which find(B) will list the nonzero entries and lu(B) will factor B using that sparse format for Land U. Only the nonzeros are computed, where ordinary (dense) MATLAB computes all the zeros too.