MRCQR stabilizes Cholesky-QR for high-condition-number matrices using a mixed-precision randomized trigonometric transform preconditioner, achieving double-precision orthogonality up to condition number 10^16 while being faster than standard methods on GPUs.
Balabanov , Randomized Cholesky QR factorizations , arXiv preprint arXiv:2210.09953, (2022)
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APLICUR uses one modest sketch to adaptively update a CUR preconditioner interleaved with LSQR iterations, delivering convergence guarantees independent of sketch size for general large-scale least-squares problems.
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Numerically Stable Cholesky-QR on GPU via Mixed-Precision Randomized Preconditioning
MRCQR stabilizes Cholesky-QR for high-condition-number matrices using a mixed-precision randomized trigonometric transform preconditioner, achieving double-precision orthogonality up to condition number 10^16 while being faster than standard methods on GPUs.
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Adaptive LSQR Preconditioning from One Small Sketch
APLICUR uses one modest sketch to adaptively update a CUR preconditioner interleaved with LSQR iterations, delivering convergence guarantees independent of sketch size for general large-scale least-squares problems.