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Lectures on Numerical Analysis by Prof. Yuji Nakatsukasa from University of Oxford:
"Stable and efficient QR factorization and least-squares solver based on CholeskyQR"

Date:

September 2nd (Mon.)

Time:

14:00-15:00

Place:

National Institute of Informatics
19F, Room 1901

Title:

Stable and efficient QR factorization and least-squares solver based on CholeskyQR

Speaker:

Professor Yuji Nakatsukasa
Mathematical Institute,
University of Oxford

Abstract:

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.

Contact:

Ken Hayami (hayami [at] nii.ac.jp)

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