Roundoff error analysis of the CholeskyQR2 algorithm in an oblique inner product

• Yamamoto Yusaku

  The University of Electro-Communications JST CREST

• Nakatsukasa Yuji

  The University of Tokyo

• Yanagisawa Yuka

  Waseda University

• Fukaya Takeshi

  JST CREST Hokkaido University

Abstract

The Cholesky QR algorithm is an ideal QR decomposition algorithm for high performance computing, but known to be unstable. We present error analysis of the Cholesky QR algorithm in an oblique inner product defined by a positive definite matrix, and show that by repeating the algorithm twice (called CholeskyQR2), its stability is greatly improved.

Journal

• JSIAM Letters

  JSIAM Letters 8 (0), 5-8, 2016

  The Japan Society for Industrial and Applied Mathematics

Keywords

• QR decomposition
• Cholesky QR
• oblique inner product
• error analysis

Details

• CRID: 1390001205300697472
• NII Article ID: 130005125235
• DOI: 10.14495/jsiaml.8.5
• ISSN: 18830617
• ISSN: 18830609
• Web Site: https://www.jstage.jst.go.jp/article/jsiaml/8/0/8_5/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed