The method of Cholesky for linear systems

  • Claude Brezinski
  • Dominique Tournès


This chapter is devoted to the method of Cholesky for solving systems of linear equations with a symmetric (and positive definite) matrix. In Section 4.1, we will introduce the method of least squares which is used for treating data generated by a topographical survey. These data have to be adjusted as explained in Section 4.2. Then, a system of linear equations is obtained. Its solution can be obtained by various methods which were in use before Cholesky’s discovery. They will be reviewed in Section 4.3. Section 4.4 is devoted to the manuscript of Cholesky. Then, it will be analyzed in Section 4.5. In Section 4.6, we will discuss other methods for linear systems which were introduced after Cholesky’s. Finally, its diffusion in the scientific community will be the subject of Section 4.7.


Linear System Arithmetical Operation Normal Equation Triangular Matrix Elimination Method 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Claude Brezinski
    • 1
  • Dominique Tournès
    • 2
  1. 1.Laboratoire Paul PainlevéUniversité des Sciences et Technologies de LilleVilleneuve d’AscqFrance
  2. 2.Laboratoire d’Informatique et de MathématiquesUniversité de La RéunionSainte ClotildeFrance

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