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Create local repository for matrix toolboxes. Step #0 done.
author Antonio Pino Robles <data.script93@gmail.com>
date Wed, 06 May 2015 14:56:53 +0200
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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1 function [Q,H] = arnoldi(A,q1,m)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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2 %ARNOLDI Arnoldi iteration
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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3 % [Q,H] = ARNOLDI(A,q1,M) carries out M iterations of the
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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4 % Arnoldi iteration with N-by-N matrix A and starting vector q1
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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5 % (which need not have unit 2-norm). For M < N it produces
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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6 % an N-by-(M+1) matrix Q with orthonormal columns and an
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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7 % (M+1)-by-M upper Hessenberg matrix H such that
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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8 % A*Q(:,1:M) = Q(:,1:M)*H(1:M,1:M) + H(M+1,M)*Q(:,M+1)*E_M',
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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9 % where E_M is the M'th column of the M-by-M identity matrix.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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10
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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11 n = length(A);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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12 if nargin < 3, m = n; end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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13 q1 = q1/norm(q1);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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14 Q = zeros(n,m); Q(:,1) = q1;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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15 H = zeros(min(m+1,m),n);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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16
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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17 for k=1:m
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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18 z = A*Q(:,k);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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19 for i=1:k
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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20 H(i,k) = Q(:,i)'*z;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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21 z = z - H(i,k)*Q(:,i);
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22 end
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23 if k < n
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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24 H(k+1,k) = norm(z);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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25 if H(k+1,k) == 0, return, end
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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26 Q(:,k+1) = z/H(k+1,k);
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27 end
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28 end