Linear operator norm maximization

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Magda Selivanovica
Magda Selivanovica 2017-6-19
Hi! So im trying to calculate linear norms: A11,A12,A1infiniy, A21,... But in having problem to find that sup, when x norm =1. So far ive found only how to calculate norm if x is given: A=A=[1 2; 3 4]; p=2; q=2; % Engine [m n]=size(A); x = rand(n,1); f = 0; fold = 1; while abs(abs(f)/abs(fold)-1) > 1e-10 % some adjustable tolerance x = x / norm(x,q); Ax = A*x; fold = f; f = norm(A*x,p); end % Display fprintf('norm(A,%d,%d) = %g\n', p, q, f)
I also tryed in maple similar: C:=multiply(A,x):N1:=norm(C,1): N2:=norm(C,2): N3:=norm(C): > n1:=norm(x,1): n2:=norm(x,2): n3:=norm(x): > A11:=Max(N1/n1): > A12:=Maximize(N1/n2)[1]: > A21:=Maximize(N2,{n1=1,n2<=1})[1]: > A22:=Maximize(N2/n2)[1]: > A13:=Maximize(N1/n3):

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