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Least squares, three ways
The normal equations, QR, and the SVD solve the same problem with very different accuracy. The difference is the square of a condition number.
Notebook: rerunning an analysis from two years ago
What it took to reproduce an old bootstrap analysis, and why its confidence interval moved in the third decimal place.
Adding up ten million numbers
Recursive summation in single precision loses four digits over ten million terms. Pairwise and compensated summation keep them for little extra work.