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If nothing else whatever field this is from has very fancy sounding jargon.

From another post on the site "I researched various different approaches to this problem and implemented the algorithms Conjugate Projected Gradient, Projected Steepest Descent, Projected Gauss-Seidel, Subspace Minimization with Conjugate Gradient, Minimum Residual and Symmetric LQ solvers, as well as Projected Gauss-Seidel with line search using the Armijo rule."

These are almost all algorithms I've either heard about or actually implemented in a graduate level numerical methods course given in a mechanical engineering department. Nothing extremely esoteric but it depends on your background. I've no clue about most classic CS algorithms (dijkstra, algo for tree structures, etc).

I ran Subspace Minimization with Conjugate Gradient on your post and find it satisfactory.

They're all various optimization technique, variations on gradient descent.

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