MATLAB: Matlab code for this type of factorization.A has a SR decomposition A = SR , where S ∈ R^ 2n ×2n is a symplectic matrix, i.e. S ^TJS = J

controlmatrix decomposition

J=[0 -I;I 0] where I∈R^ n ×n means identity matrix. R=[R11 R12;R21 R22]∈ R^ 2n ×2n , is constituted by upper triangular matrices R11 , R12 , R22 and strictly upper triangular matrix R21. diag (R11 ) =|diag (R22 )| and diag (R12 ) = 0 , then the SR decomposition is unique.

Best Answer

I'm not very acquainted with the SR decomposition (all I know about it I found just now by googling). I would suggest to take a look at what seems to be the original paper, "Matrix factorizations for symplectic QR-like methods" by Bunse-Gerstner. This seems to suggest an algorithm using other factorizations (e.g. QR) as building blocks.

I'm also tagging this Control, because it seems that this decomposition has applications in total control.

Related Solutions

MATLAB: Leverrier method to find polynomial of matrix

function c = leverrier(A)
    a=size(A,1);
    M=zeros(a);
    c=zeros(1,a+1);
    c(1)=1;    
    for k=2:a+1
        M=A*M+c(k-1)*eye(a);
        c(k)=-1/(k-1)*trace(A*M);
    end
end

MATLAB: For Ax=b, How to make LU decomposition (A=L*U) without using lu function. For example, A is nxn matrix and bis nx1 matrix.

function [L,U] = mylu(A)
n = size(A,1);
for k = 1:n
    if A(k,k)==0
        warning('LU factorization fails');
        L = []; U = []; return; 
    end
    i = k+1:n;
    A(i,k) = A(i,k)/A(k,k);
    A(i,i) = A(i,i)-A(i,k)*A(k,i);
end
L = tril(A,-1)+eye(n); U = triu(A);

Best Answer

Related Solutions

MATLAB: Leverrier method to find polynomial of matrix

MATLAB: For Ax=b, How to make LU decomposition (A=L*U) without using lu function. For example, A is nxn matrix and bis nx1 matrix.

Related Question