On the Failure of Rank-Revealing QR Factorization Software -- A Case Study
ACM Transactions on Mathematical Software (TOMS)
Accelerating geoscience and engineering system simulations on graphics hardware
Computers & Geosciences
A Global Convergence Proof for Cyclic Jacobi Methods with Block Rotations
SIAM Journal on Matrix Analysis and Applications
Novel modifications of parallel Jacobi algorithms
Numerical Algorithms
Fast dimension reduction for document classification based on imprecise spectrum analysis
Information Sciences: an International Journal
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This paper presents a new one-sided Jacobi SVD algorithm for triangular matrices computed by revealing QR factorizations. If used in the preconditioned Jacobi SVD algorithm, described in part one of this paper, it delivers superior performance leading to the currently fastest method for computing SVD decomposition with high relative accuracy. Furthermore, the efficiency of the new algorithm is comparable to the less accurate bidiagonalization-based methods. The paper also discusses underflow issues in floating point implementation and shows how to use perturbation theory to fix the imperfectness of the machine arithmetic.