ACM Transactions on Mathematical Software (TOMS)
Accelerating the SVD Block-Jacobi Method
Computing - Editorial: Special issue on GAMM – Workshop on Guaranteed Error-bounds for the Solution of Nonlinear Problems in Applied Mathematics
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
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This paper presents fast plane rotations for orthogonal similarity and orthogonal one-sided transformations. Fast rotations have the advantage that they reduce the number of square roots and multiplications. The authors' new rotations have further advantages over the existing fast rotations: they obviate the rescaling that has been necessary to guard against underflow or overflow and they give higher efficiency, especially on vector processors. An error analysis, in the case of the $QR$ decomposition, and computational results that illustrate the effects of the dynamic scaling are presented.