Homework Assignment #3

Homework Assignment - 1.2500 2 clear all n = 50 h = 1/n for i = 1:n A(i =(2 h^2(pi^2/h^2 end for i = 1:n-1 B(i =-1/h^2 end for i = 1:n-1 C(i

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1. n = input('Dimension of n of matrix:'); A = input('Center diagonal vector of length n:'); B = input('Upper Diagonal vector of length n-1:'); C = input('Lower Diagonal vector of length n-1:'); R = input('Right hand side of length n:'); B=[0,B]; L(1, 1) = A(1); U(1, 2) = C(1)/L(1, 1); Z(1) = R(1)/L(1, 1); for i = 2:n-1 L(i, i-1) = B(i); L(i, i) = A(i) - (L(i, i-1)) * (U(i-1, i)); U(i, i+1) = C(i)/L(i, i); Z(i) = (R(i)-L(i, i-1)*Z(i-1))/L(i, i); end L(n, n-1) = B(n); L(n, n) = A(n) - L(n, n-1)*U(n-1, n); Z(n) = (R(n) - L(n, n-1)*Z(n-1))/L(n, n); x(n) = Z(n); for i = n-1:-1:1 x(i) = Z(i) - (U(i,i+1) * x(i+1)); end disp('x =') disp(x) >> Crout Dimension of n of matrix:4 Center diagonal vector of length n:[2, 2, 2, 2] Upper Diagonal vector of length n-1:[-1, -1, -1] Lower Diagonal vector of length n-1:[-1, -1, -1] Right hand side of length n:[1, 0, 0, 1] x = 1.0000 1.0000 1.0000 1.0000 >> U U = 1 -0.5000 0 0 0 1 -0.6667 0 0 0 1 -0.7500 0 0 0 1 >> L L = 2.0000 0 0 0 -1.0000 1.5000 0 0 0 -1.0000 1.3333 0 0 0 -1.0000
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Unformatted text preview: 1.2500 2. clear all n = 50; h = 1/n; for i = 1:n A(i) = (2+h^2*(pi^2))/h^2; end for i = 1:n-1 B(i) = -1/h^2; end for i = 1:n-1 C(i) = -1/h^2; end for i = 1:n R(i) = 2*(pi^2)*sin(pi*i/n); end B=[0,B]; L(1, 1) = A(1); U(1, 2) = C(1)/L(1, 1); Z(1) = R(1)/L(1, 1); for i = 2:n-1 L(i, i-1) = B(i); L(i, i) = A(i) - (L(i, i-1)) * (U(i-1, i)); U(i, i+1) = C(i)/L(i, i); Z(i) = (R(i)-L(i, i-1)*Z(i-1))/L(i, i); end L(n, n-1) = B(n); L(n, n) = A(n) - L(n, n-1)*U(n-1, n); Z(n) = (R(n) - L(n, n-1)*Z(n-1))/L(n, n); x(n) = Z(n); for i = n-1:-1:1 x(i) = Z(i) - (U(i,i+1) * x(i+1)); end x y = x; plot(0:1*pi/50:49*pi/50,y) N = 50 π HW 4 Ian Chang Valentine’s Day 2008 7223076 N = 100 π 3. First you should check that your method converges. If your method converges then you need to go ahead and check the rate of convergence. Also if there is any data that you can use to check your method against, you should do that as well....
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This note was uploaded on 05/01/2009 for the course PSTAT 120A taught by Professor Mackgalloway during the Spring '08 term at UCSB.

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Homework Assignment - 1.2500 2 clear all n = 50 h = 1/n for i = 1:n A(i =(2 h^2(pi^2/h^2 end for i = 1:n-1 B(i =-1/h^2 end for i = 1:n-1 C(i

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