Numerical Linear Algebra
where the algebra stops being the arithmetic
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Ladders — page 4

A field says what an essay is about. A ladder says what else there is to say about it — the distinct arguments that stand against one idea, from the one that introduces it to the one that assumes all the others.
00.250.50.75110⁻¹110¹share of the noise placed in the matrixleast-squares error ÷ total least-squares errorequally accuratetotal leastsquares aheadordinary leastsquares aheadthe model, not the methodadvantage, all noise in b0.28advantage, all noise in A2.5seeds at each share40the same total noise at every pointand only where it sits changes

Total least squares

  1. 1 When the matrix is wrong too
1 rung · leastsquares 1112131415193111.365129.731148.096166.461probes takenrunning estimate of the tracenormal±1one probe, no errorthe exact trace99±1 variance, this matrix0±1 variance, rotated57normal variance545the same spectrum in a general basiscosts the ±1 probe its whole advantage

Trace estimation

  1. 1 Counting what cannot be looked at
1 rung · randomised

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