Abstract
For the orthonormalization of a large matrix of very slim-shape, compared from the ordinal method such as the modified Gram-Schmidt or the Householder-QR, the classical singular value decomposition method (CSVD) with orthonormality corrections has the higher locality of memory references which reduces the amount of data transfer across the storage hierarchy between the cache and the main memory or between the main memory and the external storage device, which makes the fast computation possible. From experiments on several computer systems, in certain cases the CSVD method can be several times faster than the modified Gram-Schmidt is examined.
