The way to solve a singular matrix

Question

Amad-Adeen Baiuk 2014-8-22

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https://ww2.mathworks.cn/matlabcentral/answers/151891-the-way-to-solve-a-singular-matrix

评论： Aditya Agrawal 2020-12-8

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?

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Answer 1

Mikhail 2014-8-22

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https://ww2.mathworks.cn/matlabcentral/answers/151891-the-way-to-solve-a-singular-matrix#answer_149547

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

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Amad-Adeen Baiuk 2014-8-23

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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Answer 2

John D'Errico 2014-8-23

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编辑：John D'Errico 2014-8-23

在 MATLAB Online 中打开

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

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Einat Shoval 2017-12-24

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

Aditya Agrawal 2020-12-8

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

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Answer 3

Jess 2016-3-22

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https://ww2.mathworks.cn/matlabcentral/answers/151891-the-way-to-solve-a-singular-matrix#answer_214641

在 MATLAB Online 中打开

% 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!

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Xin Shen 2019-7-10

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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