3
votes
1answer
54 views

Is there a faster way to calculate a pseudo-inverse of a matrix than using SVD that is as numerically stable as with SVD?

Is there a faster way to calculate a pseudo-inverse of a matrix than using SVD that is as numerically stable as using SVD?
0
votes
1answer
68 views

Least Square with homogeneous solution!

I've read somewhere that: $x=A^+b+(I-A^+A)Z$ is a solution for $Ax=b$ ,when is doesn't have a particular solution. where $A^+$ indicates the pseudo-inverse and $Z$ is an arbitrary vector!!! I know ...
0
votes
1answer
194 views

What is the error in Newton's Method for Matrix Inversion?

I need it to invert a matrix. Wikipedia explains that there is a generalization of the Newton Method for matrices. However, there is nothing mentioned about the error bounds. Suppose we have, as ...
3
votes
1answer
474 views

Matrix Pseudo-Inverse using LU Decomposition?

What is the step by step numerical approach to calculate the pseudo-inverse of a matrix with M rows and N columns, using LU decomposition? So far, I have found this, but it uses singular value ...
4
votes
1answer
92 views

solve $ y = (A+B^{-1})x $ for $x$

I wish to solve numerically for $x$, $$ y = (A+B^{-1})x $$ with $A, B$ positive definite. So, $$ x = (A+B^{-1})^{-1}y $$ I would like to avoid calculating $B^{-1}$ since that's generally bad. ...
1
vote
3answers
130 views

Compute $\mathbf v \mathbf A^{-1}\mathbf v^\top$ in a numerically stable way

I've read that you should avoid computing a matrix inverse, as you generally don't need to, but I don't know the best way to avoid it. I need to compute: $$x = \mathbf v \mathbf A^{-1}\mathbf ...