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2 results

  • 3 - Systems of Linear Equations

  • from Part I - Numerical Linear Algebra
  • Abner J. Salgado, University of Tennessee, Knoxville, Steven M. Wise, University of Tennessee, Knoxville
  • Book:
    Classical Numerical Analysis
    Published online:
    29 September 2022
    Print publication:
    20 October 2022, pp 31-72

  • Summary

    We study the solution of square systems of linear equations with a nonsingular matrices, we provide sufficient conditions for the classical Gaussian elimination with pivoting to proceed without failure. We introduce the LU factorization of a matrix, and several of its variants, like Cholesky factorization.

  • 1 - Preliminaries

  • David C. Vella, Skidmore College, New York
  • Book:
    Invitation to Linear Programming and Game Theory
    Published online:
    11 March 2021
    Print publication:
    11 March 2021, pp 1-62

  • Summary

    We introduce the mathematical modeling process. We also set the stage for the rest of the book by discussing systems of linear equations and their solutions, matrices, Gauss-Jordan elimination, linear combinations of vectors, basis vectors of Euclidean space, and their connection to basic solutions of a linear system. We conclude with simple optimization problems with quadratic functions.