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 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.