Matrix Numerical Methods for Solving Systems of Linear Equations in C++

A system of equations is solved using the following algorithms in numerical methods, coded in C++ language:

• Gauss method – LU decomposition
• Gauss Method – Maximum Pivot
• Cholesky method
• Gauss-Seidel method

HISTORY

• Version 2 – 02-IV-2024
  • Code is updated and improved
  • Comments are translated from Spanish to English
  • std::vector is used instead of arrays, and in this way the limitation that did not allow solving systems of equations with more than 10 unknown variables is eliminated.
  • Improvements in the coding of the Gauss Seidel and Cholesky algorithms.
  • Finished replacing all arrays with std:vector
  • An alert message is added informing when the Cholesky method cannot be applied
  • The code is modernized, converting it into the CMatrixSolvingLinearEq class
  • Traces of old C functions, such as printf, cprintf, fabs, etc… are removed and replaced with their modern equivalents
  • Some missing comments and the names of the CMatrixSolvingLinearEq methods are translated into English.
  • Unnecessary files are removed
  • The option is added to generate the elements of matrices A and B randomly, only defining the order of the matrix and indicating whether it will be diagonally dominant. If you create a diagonally dominant matrix, it can be successfully processed.
  • Modifications are added to the History version
  • The roots are shown in the Gauss-Seidel method as long as this method converges.
  • In the Cholesky method, information messages are added about whether the method converges or does not converge.
  • The user is asked whether or not he wants to display the LU matrices, because for a large dimension of A, the display process is slow.
  • A chronometer is added to measure the time that each method takes, and the seconds that each method has taken to process the solution are shown, in order to obtain a point of comparison between the efficiency of the algorithms.
• Version 1 – 30-XI-1999
  • First version for Borland C++ 3.1 and Turbo C 3.0