Matrix-free — where it appears
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
Counting what cannot be looked at
The trace is n additions and one of the most expensive quantities in the subject to estimate, because the matrices whose trace is wanted are never stored. Hutchinson's estimator is unbiased with one line of algebra — and its variance depends on which random vector is used, by a factor that is a property of the matrix, and on a diagonal matrix one choice is exact from the first probe and the other is not.
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.
CancellationCondition numberGeneralised cross validationHutchinson's estimatorInfluence matrixKrylov subspaceLsqrPreconditioningProbabilistic boundsRandom projectionSketch and preconditionSketch-and-solve