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## Main Question or Discussion Point

Does anyone happen to know a good algorithm for a numerical Karhunen-Loeve transformation for tensors?

Specifically, I'm trying to solve for the eigentensors of a correlation bitensor, along the lines of

[tex]\int_{-\infty}^{\infty} d^4x' \, C_{abc'd'}(x,x') \phi^{c'd'}(x') = \lambda \phi_{ab}(x) \,[/tex] where the primes represent indices which transform at the point [itex]x'[/itex]. What I need to find is a numerical algorithm to solve this equation with support on a lattice of points.

I have a good handle on how to do this for scalars, but can't figure out how to adapt the algorithm to handle tensor expressions. Does anyone have any experience with this, and if so could you give me some pointers?

Specifically, I'm trying to solve for the eigentensors of a correlation bitensor, along the lines of

[tex]\int_{-\infty}^{\infty} d^4x' \, C_{abc'd'}(x,x') \phi^{c'd'}(x') = \lambda \phi_{ab}(x) \,[/tex] where the primes represent indices which transform at the point [itex]x'[/itex]. What I need to find is a numerical algorithm to solve this equation with support on a lattice of points.

I have a good handle on how to do this for scalars, but can't figure out how to adapt the algorithm to handle tensor expressions. Does anyone have any experience with this, and if so could you give me some pointers?