@MISC{Lang96usinglevel, author = {Bruno Lang and Lang B}, title = {Using Level 3 BLAS in the QR Algorithm}, year = {1996} }

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Abstract

1.41> , . . . , ae 1 max1 , ae 2 1 , ae 2 2 , . . . . If the eigenvectors of T are sought, too, then the same rotations must also be applied to another (full) matrix U . For larger matrices, updating U by far dominates the work on T . The simplest update strategy is to apply each rotation to U when it is generated. In the LAPACK [1] implementation, the update is delayed until a sweep is completed, thus enabling the use of a BLAS 2-like routine for applying a sequence of rotations. By further delaying the update until some number n b of sweeps on T are completed, we may even use matrix-matrix products to do the vast majority of the operations [5]. To this end we note that the data dependence in the update is somewhat weaker than in the work on T , see Fig. 1. Since the