.. _R6.03.01:

**r6.03.01** Resolution of non-regular systems by a method of decomposition into singular values
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**Summary**:

This document is devoted to the resolution of systems of non-regular linear equations. The matrices taken into account may be square, non-invertible, or rectangular.

After recalling the theoretical framework of solutions in the sense of least squares, we focus the paper on the method by decomposition into singular values, which provides, on the one hand, a tool for diagnosing the degree of regularity of the system, and, on the other hand, a family of resolution algorithms that are both more general and more stable than those deriving from the normal equation approach.

Finally, we detail the algorithm implemented in the*Code_Aster* which resolves the equivalent functionality of the *Nag* library (F04 JDF for version 12 and F04 JDE for version 15) used for modeling the metallurgical behavior of steels [:ref:`R4.04.01 <R4.04.01>`].




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.. toctree::
    :maxdepth: 2
    :numbered:

    Introduction
    Solution_d_un_syst_me_lin_aire_rectangulaire
    Valeurs_singuli_res
    R_solution_d_un_syst_me_lin_aire_rectangulaire
    Algorithme_SVD_pour_la_r_solution_d_un_syst_me_lin_aire__qui_ou_sous-contraint
    Bibliographie
    Description_des_versions_du_document