Error analysis of some techniques for updating orthogonal decompositions

Paige, C. C.

doi:10.1090/S0025-5718-1980-0559196-9

Error analysis of some techniques for updating orthogonal decompositions
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Math. Comp. 34 (1980), 465-471 Request permission

Abstract:

We consider accurate and efficient methods for updating the result of the transformation $C = BQ$, Q orthogonal, of a given matrix B when Q is available. Adding or deleting a row, or adding a column of B leads to a continuation of the original transformation, and as such is numerically stable. In particular, we discuss a well-known method for updating when a column of B is deleted, and show that it is as numerically stable as the problem allows. The results extend to two-sided transformations of the form $C = {Z^T}BQ$. The methods and analyses are independent of the form or rank of B and C, and so are widely applicable.

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