R. W. Farebrother, Remark AS R17: Recursive Residuals-A Remark on Algorithm AS 75: Basic Procedures for Large, Sparse or Weighted Linear Least Squares Problems, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 25, No. 3 (1976), pp. 323-324
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R. W. Farebrother (1976) studied this question.