Abstract
This paper concerns thin QR decomposition in an oblique inner product. Cholesky QR is known as a fast algorithm for thin QR decomposition. On the other hand, this algorithm is not applicable for ill-conditioned matrices. The preconditioned Cholesky QR algorithms named LU-Cholesky QR for thin QR decomposition are recently proposed. We apply these preconditioning techniques to thin QR decomposition in an oblique inner product.
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