Sketch and precondition — where it appears
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
Also named here as sketch-and-solve — the same set of essays touches all of them, so they are one junction rather than several.
Randomisation does not create structure
On a matrix whose singular values are all equal, a rank-ten randomised approximation has error 1.0 — and so does the optimal deterministic one. Neither achieved anything, and only one of them is usually sold with the implication that it might.
The sketch that is not the answer
Sketch-and-solve throws away the original problem and keeps the small one's answer, which is why its answer moves with the seed. Use the same sketch as a preconditioner instead and the condition number the iteration sees is the same number at every κ from a hundred to ten billion — identically the same, to nine digits, because the spectrum cancels out of it.
Named alongside it
The objects these essays reach for when they reach for this one.
Sketch-and-solveSketchingCondition numberKrylov subspaceLow-rank approximationLsqrMatrix-freePreconditioningRandomised SVDResidualSingular value decompositionSingular values