Hybrid regularisation — 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 projected problem — the same set of essays touches all of them, so they are one junction rather than several.
The step that stops mattering
Regularise the problem the iteration has built rather than the problem it was given, and the error curve stops turning. The unregularised run ends 1,127 times above its own best; the same run with a penalty inside it ends 1.000000000003 times above.
A parameter chosen on a smaller problem
Inside a hybrid method the regularisation parameter is chosen on a 25×24 problem rather than a 64×64 one. The rule that reads a residual transfers exactly; the rule that reads a trace is biased by exactly two grid steps at twenty-four steps and one at forty, at every noise level from 10% to 0.1%.
Named alongside it
The objects these essays reach for when they reach for this one.
Golub kahan bidiagonalisationIll posed problemProjected problemStopping criterionDiscrepancy principleGeneralised cross validationInfluence matrixIterative regularisationOracleParameter choiceReorthogonalisationRitz values