The way to solve a singular matrix

Hi

There is any one know how the method to decompose the singular square matrix using Matlab. Someone told me the Matlab have something like a ready Forthran subroutine. Does anyone know how to use it in Matlab?

Answer 1

[Mikhail]

U need SVD? http://www.mathworks.com/help/matlab/ref/svd.html

[Amad-Adeen Baiuk]

thanks Mikhail. but how can apply the svd to find the inverse of square singular matrix in order to solve the set of linear system.

Answer 2

[John D'Errico]

help pinv

Not much more to say, since you give very little info to help you on. Note that computing the inverse of a matrix is almost never recommended. The backslash operator is a better choice always than inv. But pinv is a good tool for this purpose, when backslash (and surely also inv) will fail.

A = ones(2);
A\[1;1]
Warning: Matrix is singular to working precision. 
ans =
   NaN
   NaN

inv(A)*[1;1]
Warning: Matrix is singular to working precision. 
ans =
   Inf
   Inf

pinv(A)*[1;1]
ans =
          0.5
          0.5

[Einat Shoval]

Thank you so much for this!! Was stuck on this for two days now until I found your answer :)

[Aditya Agrawal]

Thankyou so much! I had the same issue and your solution works!

Answer 3

[Jess]

% Goal: solve A*x == b for x

% Set up some matrix A (I used a sparse matrix) -- do yourself

% Set up the vector b  -- do yourself

% Perform SVD on A
[U,S,V] = svd(A);

% A == U*S*V'  % Not needed, but you can check it yourself to confirm

% Calc number of singular values
s = diag(S);   % vector of singular values
tolerance = max(size(A))*eps(max(s));
p = sum(s>tolerance);

% Define spaces
Up = U(:,1:p);
%U0 = U(:,p+1:Nx);
Vp = V(:,1:p);
%V0 = V(:,p+1:Nx);
%Sp = spdiags( s(1:p), 0, p, p );
SpInv = spdiags( 1.0./s(1:p), 0, p, p );

% Calc AInv such that x = AInv * b
AInv = Vp * SpInv * Up';

x = AInv * b;   % DONE!

[Xin Shen]

When I tried your idea to solve my problem, I got an error "SVD does not support sparse matrices. Use SVDS to compute a subset of the singular values and vectors of a sparse matrix". Does SVDS work for your idea?