An efficient implementation of the block Gram–Schmidt method

The block Gram–Schmidt method computes the qr factorisation rapidly, but this is dependent on block size m. We endeavor to deter-mine the optimalm automatically during one execution. Our algorithm determines m through observing the relationship between computa-tion time and complexity. Numerical experiments show that our pro-posed 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. Subject class: 65F10, 65M1