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Numerical Solution of Systems of Algebraic Equations

In: Numerical Methods and Optimization

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  • Jean-Pierre Corriou

    (University of Lorraine)

Abstract

The solution of systems of linear or nonlinear equations is searched for by many different techniques. First, linear systems considered under matrix form are solved by Gauss and Gauss–Jordan algorithms. Then, techniques for particular matrices are exposed, such as LDL T factorization, Cholesky decomposition, and singular value decomposition. The case of least squares for linear overdetermined systems, iterative techniques for large systems such as Jacobi, Gauss–Seidel, and the case of tridiagonal systems are treated in detail. The solution of nonlinear systems is given by Newton–Raphson’s method and optimization techniques are mentioned. These latter occupy specific chapter 9 in the optimization part of the book. All the methods are illustrated by significant numerical examples.

Suggested Citation

  • Jean-Pierre Corriou, 2021. "Numerical Solution of Systems of Algebraic Equations," Springer Optimization and Its Applications, in: Numerical Methods and Optimization, chapter 0, pages 149-187, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-89366-8_5
    DOI: 10.1007/978-3-030-89366-8_5
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