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The way to solve a singular matrix

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Amad-Adeen Baiuk
Amad-Adeen Baiuk am 22 Aug. 2014
Kommentiert: Aditya Agrawal am 8 Dez. 2020
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?

Antworten (3)

Mikhail
Mikhail am 22 Aug. 2014
  1 Kommentar
Amad-Adeen Baiuk
Amad-Adeen Baiuk am 23 Aug. 2014
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.

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John D'Errico
John D'Errico am 23 Aug. 2014
Bearbeitet: John D'Errico am 23 Aug. 2014
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
  2 Kommentare
Einat Shoval
Einat Shoval am 24 Dez. 2017
Thank you so much for this!! Was stuck on this for two days now until I found your answer :)
Aditya Agrawal
Aditya Agrawal am 8 Dez. 2020
Thankyou so much! I had the same issue and your solution works!

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Jess
Jess am 22 Mär. 2016
% 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!
  1 Kommentar
Xin Shen
Xin Shen am 10 Jul. 2019
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?

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