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<p>Recently, the <Emphasis FontCategory="SansSerif">shiftedCholeskyQR3</Emphasis> algorithm has been proposed as an optional choice of the orthogonalization algorithms. We extend the error analysis result for oblique inner product and show that the new error bound is optimal. We also discuss the loss of orthogonality and verify our conclusions through numerical experiments.</p>

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An optimal error bound for shiftedCholeskyQR3 in oblique inner product

  • 期刊论文

  • 发表日期：

    2025年6月16日

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  • Weiguo Gao,
  • Rentao Xu

摘要

Recently, the shiftedCholeskyQR3 algorithm has been proposed as an optional choice of the orthogonalization algorithms. We extend the error analysis result for oblique inner product and show that the new error bound is optimal. We also discuss the loss of orthogonality and verify our conclusions through numerical experiments.