Function note

LINEST's Householder reflector stores each step from the x87 unit

FUNC.LINEST · FUNC.LOGEST

FN-LINEST-001: LINEST's Householder reflector stores each step from the x87 unit

Detail for matching Excel's bits · measured · recorded 2026-11-04

In Excel's QR route the reflector arithmetic behaves as stored precision-64 steps: v0 = x0 - alpha, v'v, each dot-product term, f = 2t/v'v, and a - f*v. With this change the row below gets Excel's last bits, where a plain binary64 reflector does not.

Call and input routeInputsExcelCorrect valueRecorded in
=INDEX(LINEST({-17.979;-0.126;8;-5;1.7;37;12.4;14.46;-8;24.2},{20.8,50;34,23.41;38.875,-17.7;4.863,36.9;42.1,6;-14.55,44.41;-4.57,-12.96;-9.909,2.589;47.549,42;54.9,-17.63},TRUE,TRUE),2,1)
formula-literal
As typed0.19054144531344644
0x3fc863a97e13b089
—Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA

Basis: Gains 11 recorded answers and loses none over the 3,944 regression rows of the corpus; 35 selections from two fits were checked directly.

Open: Norm, rank, mean, pivot and back-substitution policies are not identified. 48 fixed rank policies and 240 rounded Gram/LDL rank labels are contradicted by the 241 recorded degrees-of-freedom observations.

Evidence and capture sources

Machine-readable note records