Error analysis of $QR$ updating with exponential windowing

G. W. Stewart
1992 Mathematics of Computation  
Exponential windowing is a widely used technique for suppressing the effects of old data as new data is added to a matrix. Specifically, given an n x p matrix Xn and a "forgetting factor" ß € (0, 1 ), one works with the matrix diag(/i'1_1, ß"~2, ... , \)Xn ■ In this paper we examine an updating algorithm for computing the QR factorization of diag(/j"-1, ß"~2 , ... , \)X" and show that it is unconditionally stable in the presence of rounding errors.
doi:10.1090/s0025-5718-1992-1134738-1 fatcat:lnilu2cefzdlllzfxyilqxqlfm