An efficient implementation of the block Gram--Schmidt method


  • Yoichi Matsuo School of Fundamental Science and Technology, Graduate School of Science and Technology, Keio University
  • Takashi Nodera Department of Mathematics, Faculty of Science and Technology, Keio University



block Gram-Schmidt algorithm, optimal block size, parallel computing


The block Gram--Schmidt method computes the QR factorisation rapidly, but this is dependent on block size \(m\). We endeavor to determine the optimal \(m\) automatically during one execution. Our algorithm determines \(m\) through observing the relationship between computation time and complexity. Numerical experiments show that our proposed algorithms compute approximately twice as fast as the block Gram--Schmidt method for some block sizes, and is a viable option for computing the QR factorisation in a more stable and rapid manner. References
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