A block Gram-Schmidt algorithm with its application

Gram-Schmidt algorithm is one of the fundamental methods in linear algebra,which is mainly used to compute QR decomposition. The classical and modified Gram-Schmidt are both based on level 1 or level 2 BLAS operations which have low cache reuse. In this paper,a new block Gram-Schmidt algorithm is proposed. The new algorithm ensures the orthogonality of resulting matrix Q is close to machine precision and improves performance because of using level 3 BLAS. Numerical experiments confirm the favorable numerical stability of the new algorithm and its effectiveness on modern computers.