Solving A X = B equation with ITensor

I am wondering of one can use ITensors to solve linear equations in the form of
A X = B

where all of the components are tensor networks or high order tensors in some compressed format? Or if not does anybody know a package that does that?

My tensors represent high order polynomials of large number of variables, hence they a symmetric. This needs some compressed format, so tensor networks, tensor train or H-tucker are the candidates. I need some machinery that can substitute polynomials into each other, multiply them and then solve these multi-linear equations.

Many thanks…

Developer of ITensor here. Sorry for the late response, I don’t check Julia discourse for ITensor questions as often as I should. You can also post questions on the ITensor support forum (ITensor Support Q&A) which we check more often.

I would recommend using KrylovKit’s linsolve function in conjunction with ITensors.jl. You can find some minimal examples of that here: ITensors.jl/examples/krylov_methods/gmres at main · ITensor/ITensors.jl · GitHub

If this doesn’t cover your use case please let us know.

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