percusse
  • Member for 5 years, 4 months
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Matrix Balancing Algorithm
Accepted answer
7 votes

Took me quite a while to figure this out and as usual it becomes obvious after you find the culprit. After checking the problematic cases reported in David S. Watkins. A case where balancing is ...

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Fast multiplication of highly structured matrix
4 votes

Late answer but the matrix can be thought of the following sum of rank-$2$ matrices which allows for having smaller block sizes as the number of blocks increase. $$ \begin{align*} c_{20}=\left( \...

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Are there any packaged routines (in lapack or elsewhere) for inverting a banded matrix?
4 votes

Well, other than the usual "don't invert your matrices unless you need the inverse itself" you can still use the banded routines ?gbtrf and then use ?gbtrs with the right hand side being an identity ...

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Discrete-time input matrix when one of the eigenvalues of the system matrix is zero
1 votes

That equivalence is only valid if $A$ is invertible, hence it is a result but not a definition. This is typically done via the following relation $$ \exp\left(\begin{bmatrix}A & B\\0 &0\end{...

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How to preserve or recover states meanings in canonical state-space realizations
1 votes

No this is not possible. And actually, it is a good practice to not to rely on this type of inferences. Well before anything they tend to get in the way and certain operations are not structure ...

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What is the difference in the pivoting strategies between LAPACK's dpstrf and dpst2 and why?
1 votes

The difference is which BLAS level they are utilizing. TRF is BLAS3 and TF2 is BLAS2. BLAS level 3 routines, roughly speaking, optimized for computers with cache memory such that they can perform ...

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Approach to handle a quadratic constraint xy <= z
1 votes

If this is the only relevant part of your problem, you can write this as a semidefinite program. Since $x_1, x_2$ do not appear individually you can treat it as a square of a positive number then your ...

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