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Reconstructing householder vectors from tall-skinny QR

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  1. The standard householder QR algorithm and Tall-Skinny QR: differences
  2. 1D parallel algorithms
    1. 1 D Householder QR
    2. 1 D Tall Skinny QR TSQR
    3. LU decomposition of A - R
    4. Cholesky-QR decomposition
  3. 2D parallel algorithms
    1. 2D block-cyclic householder QR
    2. Communication avoiding CAQR
    3. Butterfly CAQR

The present paper deals with the fact that the output of TSQR algorithm is not represented as householder format, hence was born the idea to provide a new version of TSQR algorithm while taking advantage of its multiple benefits such as: communication efficiency, less computational cost In addition, this algorithm is considered stable numerically, as is proven by many experiments.

This paper describes also some of the parallel algorithms which are based on the householder representation, and it presents alternatives to the householder reconstruction algorithm, but they suffer from numerical stability issue.

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