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<p>This paper concentrates on the column pivoting quaternion Householder QR factorization, and considers its accuracy and stability. Firstly, we provide some floating-point operation rules related to the quaternion Householder transformation. Then, by analysing roundoff errors for parameters in the quaternion Householder transformation, we present the backward roundoff error for the column pivoting quaternion Householder QR factorization. Finally, we research the backward roundoff error for the quaternion least squares problem with column full rank.</p>

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Accuracy and stability of the column pivoting quaternion Householder QR factorization

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • Fengxia Zhang,
  • Yuqing Zhang,
  • Zhihan Zhou,
  • Zixiang Meng,
  • Ying Song,
  • Musheng Wei

摘要

This paper concentrates on the column pivoting quaternion Householder QR factorization, and considers its accuracy and stability. Firstly, we provide some floating-point operation rules related to the quaternion Householder transformation. Then, by analysing roundoff errors for parameters in the quaternion Householder transformation, we present the backward roundoff error for the column pivoting quaternion Householder QR factorization. Finally, we research the backward roundoff error for the quaternion least squares problem with column full rank.