A Survey of Numerical Aspects of Plane Rotations
Sven J. Hammarling · MIMS EPrints (University of Southampton) · 1977
In recent years the use of plane rotations in orthogonal factorizations has been increasing in popularity. This is in part due to modifications which enable computations with plane rotations to be carried out more quickly and in part due to the use of plane rotations in updating matrix factorizations and in other sparse applications. A review of Jacobi, Givens and modified plane rotations and of products of plane rotations is given. The review includes discussion of the computational details required to avoid underflow and overflow when computing plane rotations, storage of plane rotations and the stability of plane rotations. Mention is also made of the possibility of using plane rotations for pivoting.