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2008.69: A Survey of Numerical Aspects of Plane Rotations

2008.69: Sven Hammarling (1977) A Survey of Numerical Aspects of Plane Rotations. Middlesex Polytechnic Report, Maths (1). pp. 1-35.

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Abstract

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.

Item Type:Article
Uncontrolled Keywords:Givens plane rotations; Jacobi rotations; error analysis
Subjects:MSC 2000 > 15 Linear and multilinear algebra; matrix theory
MSC 2000 > 65 Numerical analysis
MIMS number:2008.69
Deposited By:Sven Hammarling
Deposited On:01 July 2008

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