Lectures on Numerical Analysis by Prof. Yuji Nakatsukasa from University of Oxford:
"Stable and efficient QR factorization and least-squares solver based on CholeskyQR"
September 2nd (Mon.)
National Institute of Informatics
19F, Room 1901
Stable and efficient QR factorization and least-squares solver based on CholeskyQR
Professor Yuji Nakatsukasa
University of Oxford
CholeskyQR is an efficient algorithm for computing the QR factorization that is not backward stable and has been rarely used. However, by regarding a CholeskyQRlike step as a means to improve the conditioning, we can derive stable and efficient algorithms applicable to ill-conditioned matrices with κ(A) = O(1/u). Such algorithms are attractive particularly when working with a non-standard inner product (e.g. B-orthogonal, quasimatrices). I will also discuss the use of CholeskyQR for solving (moderately ill-conditioned) least-squares problems, which results in a 5x speedup compared with a standard solver based on Householder QR, with comparable accuracy. Based on joint work with T. Fukaya, R. Kannan, Y. Yamamoto and Y. Yanagisawa.
Ken Hayami (hayami [at] nii.ac.jp)