Concept

Truncation — where it appears

Discarding the smallest part of a decomposition to obtain a cheaper representation. What it costs is computable from what was discarded, which is the whole reason a decomposition with an ordered spectrum is worth having.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

The direction the error leans

The size of one rounding error is set by the precision. How ten thousand of them combine is set by something else entirely — the rounding mode — and the fitted exponents are 0.47 for round-to-nearest and 1.01 for round-toward-infinity, on identical data at identical precision.

arithmetic · rounding

An iterate that must be made smaller

Applying a Kronecker-sum operator to a low-rank iterate multiplies its ranks by d and adding two of them adds their ranks, so a solver in a compressed format cannot keep what it produces. Every step is followed by a truncation — and whether that truncation is a floor on the residual depends on the right-hand side rather than on the truncation.

iterative · low rank iteration

Named alongside it

The objects these essays reach for when they reach for this one.

Conjugate gradients Curse of dimensionality Directed rounding Error accumulation IEEE 754 Interval arithmetic Kronecker sum Krylov subspace Low-rank approximation Model problem Recompression Residual

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