An Efficient Scheme for the Co-diagonalization of a Symmetric Matrix by Givens' Method in a Computer with a Two-level Store

The Givens' process, as it is commonly performed, requires simultaneous rapid access both to rows and to columns of the matrix. By running in parallel the various rotations which produce a row of zeros it is possible to reduce the number of scans of the matrix by a factor of order n. The scanning required is then less than that for Householder's process, which is, however, faster in other ways. The number of multiplications and the rounding errors for the modified Givens' process are the same as when the rotations are carried out sequentially, but on Mercury there is an overall gain in speed by a factor of 7 for matrices of order 96.