# Tag Info

Accepted

### Why is it that SVD routines on nearly square matrices run significantly faster than if the matrix was highly non square?

You are asking for a full (dense) SVD, which also needs to generate the unitary components of $U$ and $V$ which correspond with the null space of your input. for the $1000 \times 800$ case, your input ...
• 2,794

### How much regularization to add to make SVD stable?

The singular value decomposition for a symmetric matrix $A=A^{T}$ is one and the same as its canonical eigendecomposition (i.e. with an orthonormal matrix-of-eigenvectors), while the same thing for a ...
• 2,485
Accepted

### Real-world applications of eigendecomposition?

You can compute analytic functions of matrices using the eigendecomposition (or more generally by using the Jordan normal form in case the matrix is defective), you cannot do so with the singular ...
• 2,162
Accepted

### Why is matrix inversion unstable when svd is stable?

The big issue is the condition number, which is defined as the ratio of the largest and smallest singular values. Suppose we expect: $$S = \begin{bmatrix} 10^{-15}\\ &1 \end{bmatrix}$$ If we ...
• 2,794
Accepted

### Why are all eigen solvers iterative?

There is simply no closed-form expression in terms of the four operations and radicals for the eigenvalues of a matrix greater than $4\times 4$. This follows from the facts that (1) there are ...
• 11.4k
### Robust algorithm for $2 \times 2$ SVD
I needed an algorithm that has little branching (hopefully CMOVs) no trigonometric function calls high numerical accuracy even with 32 bit floats We want to calculate $c_1, s_1, c_2, s_2, \sigma_1$ ...