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The Futhark team explains why their compiler's GPU pipelines force all arrays into GPU memory, making sequential CPU-side work (like greedy distance-2 graph colouring for sparse Jacobians) three orders of magnitude slower, and describes a hack that allows keeping some functions off the GPU while still exploiting GPU parallelism for the rest of the program.
The article derives the column elimination tree for the right-looking sparse Cholesky algorithm, explaining how it predicts fill-in and task dependencies without performing dense factorization.