High-performance up-and-downdating via householder-like transformations

We present high-performance algorithms for up-and-downdating a Cholesky factor or QR factorization. The method uses Householder-like transformations, sometimes called hyperbolic Householder transformations, that are accumulated so that most computation can be cast in terms of high-performance matrix-matrix operations. The resulting algorithms can then be used as building blocks for an algorithm-by-blocks that allows computation to be conveniently scheduled to multithreaded architectures like multicore processors. Performance is shown to be similar to that achieved by a blocked QR factorization via Householder transformations.

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