I saw that the MatrixEquations.jl package was released to reproduce some solvers related to Riccati and Lyapunov equations, linked with the SLICOT library.

Are there any plans to link the Toeplitz specialized solvers from SLICOT to a julia package ?

Does this package offer what you need?

I am currently using this package to form some toeplitz matrices, but as far as I understand the code, there are also some solvers shipped, yet they do not seem to call SLICOT.

I am particulrly interested in the solution of block Toeplitz matrices problems as with e.g MB02ID from SLICOT, but I did not see anything about block Toeplitz matrices in ToeplitzMatrices.jl

I’m not aware of any package targeting this particular matrix structure, but

and the other packages in JuliaMatrices might be able to solve this problem efficiently, maybe by composing a toeplitz matrix with a block array etc.

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Do you mean that with julia the composition of matrix types may lead to performance improvements ? As in e.g. `BlockDiagonal(Toeplitz(Array)`

will optimize output computation using both blokc matrix and Toepitz matrices ?

I am not familiar with the internals of BlockArrays, but if their backsolve is implemented in terms of backsolve on the blocks (I don’t know if this is feasible) then yes, the composition will be performant.

They do have a bandedBlockBandedMatrix, so they might have some custom solvers for that.