Misc,

Precise Solutions for Overdetermined Least Squares Problems

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Stanford 50 -- Eighth Bay Area Scientific Computing Day, (March 2007)

Abstract

Linear least squares (LLS) fitting is the most widely used data modeling technique and is included in almost every data analysis system (e.g. spreadsheets). These software systems often give no feedback on the conditioning of the LLS problem or the floating-point calculation errors present in the solution. With limited use of extra precision, we can eliminate these concerns for all but the most ill-conditioned LLS problems. Our algorithm provides either a solution and residual with relatively tiny error or a notice that the LLS problem is too ill-conditioned.

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