# Tag Info

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### why is A*v+B*v faster than (A+B)*v?

Except for code which does a significant number of floating-point operations on data that are held in cache, most floating-point intensive code is performance limited by memory bandwidth and cache ...
Accepted

### Why do we usually not want the eigenvalues of non-symmetric matrices?

Stability under perturbations Let $E$ be a perturbation such that $\|E\| \leq \varepsilon$. If $A$ is symmetric, then the eigenvalues of $A+E$ are at a distance $\varepsilon$ from those of $A$. (Bauer-...
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### In FEM, why is the stiffness matrix positive definite?

The property follows from the property of the corresponding (weak form of the) partial differential equation; this is one of the advantages of finite element methods compared to, e.g., finite ...

### why is A*v+B*v faster than (A+B)*v?

Your code is limited by memory bandwidth. For trivial math, it's often better to count memory accesses rather than flops. You'll get the following table: ...

### Robust algorithm for $2 \times 2$ SVD

See https://math.stackexchange.com/questions/861674/decompose-a-2d-arbitrary-transform-into-only-scaling-and-rotation (sorry, I would have put that in a comment but I've registered just to post this ...

### Rule of thumb for sparse vs dense matrix storage

For what it is worth, for random sparse matrices of size 10,000 by 10,000 vs. dense matrices of the same size, on my Xeon workstation using MATLAB and Intel MKL as the BLAS, the sparse matrix-vector ...
### 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 $c_1, s_1, c_2, s_2, \sigma_1$ ...