josdejong/mathjs

Schur result not quasi upper triangular

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#3,600 建立於 2025年11月22日

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 (3 留言) (0 反應) (0 負責人)JavaScript (13,832 star) (1,298 fork)batch import
bugcategory:numericalhelp wanted

描述

Describe the bug A clear and concise description of what the bug is.

I think sometimes Schur returns a matrix that isn't quasi upper triangular.

To Reproduce Generic orthonormal matrices seem to create a problem. For example:

math.matrix([
      [-0.03591206220229135, -0.09100469507870354, 0.9952027277203429],
      [-0.3802068171617618, -0.9197139315803332, -0.09782157349362577],
      [0.9242040358990549, -0.38189583596928406, -0.0015717815434243287]
    ])

Possibly mathjs is running QR without a Wilkinson/Francis shift strategy?

Happy to contribute a PR on this if I'm not hallucinating the problem :).

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前置要求
Numerical linear algebramathjs code structure
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研究方向
Investigate the Schur decomposition implementation in mathjs, likely in the linear algebra module (e.g., src/function/algebra/schur.js or similar). Check if the QR algorithm used includes a shift strategy (e.g., Wilkinson shift or Francis double shift). The issue author suggests that the absence of such shift may cause the result to not be quasi upper triangular. Consider implementing the shift or verifying the existing code. The linked issue comments may provide additional clues.