.. _sphx_glr_api_gallery_linalg_stability:

Numerical stability
--------------------

The condition number: how much a linear system amplifies errors in its
data, and why least squares via the normal equations squares it while
QR does not.


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    <div class="sphx-glr-thumbcontainer" tooltip="kappa_2(A) = sigma_max / sigma_min bounds how much a relative perturbation of the data can grow in the solution of A x = b, whichever algorithm solves it: expect to lose about log10(kappa) digits. The same number explains why least squares through the normal equations A^T A x = A^T b is fragile -- kappa(A^T A) = kappa(A)^2 -- while QR works with kappa(A) itself.">

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  :doc:`/api/gallery/linalg/stability/plot_01_condition_number`

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      <div class="sphx-glr-thumbnail-title">Turing's condition number: how much a linear system amplifies error</div>
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.. toctree::
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   /api/gallery/linalg/stability/plot_01_condition_number