Matrix prerequisities for Gauss elimination

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SUMMARY

The discussion centers on the prerequisites for applying Gauss elimination in solving linear equations, particularly regarding the global stiffness matrix. It is established that a non-zero diagonal is essential for the algorithm to function correctly; if any diagonal term is zero, the algorithm exits prematurely. The user expresses concern that their global stiffness matrix may be ill-conditioned due to this issue. The suggestion is made to separate zeroes from the matrix before applying the Gauss elimination method.

PREREQUISITES
  • Understanding of linear algebra concepts, specifically matrix operations.
  • Familiarity with Gauss elimination method for solving linear equations.
  • Knowledge of matrix conditioning and its implications on algorithm performance.
  • Experience with constructing global stiffness matrices in finite element analysis.
NEXT STEPS
  • Research techniques for handling zero diagonal elements in matrices.
  • Learn about matrix conditioning and its impact on numerical stability.
  • Explore alternative methods to Gauss elimination, such as LU decomposition.
  • Investigate best practices for constructing global stiffness matrices in finite element methods.
USEFUL FOR

Mathematicians, engineers, and computer scientists working with linear equations, particularly those involved in numerical methods and finite element analysis.

Ronankeating
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hi all,

Is there any matrix pre-requisities for Gauss elimination. Working on linear equations, I think I 've composed the global(stiffness) matrix of the LHS of linear equation.And found on the net the working code which uses Gauss elimination method, in the code beginning it checks non-zero values of diagonal term, if it founds algorithm exits.
Since I'm not fully conversant everything in depth, I assume that none of the diagonal products shouldn't be zero and therefore my global stiffness matrix is ill conditioned?

Any comment will be appreciated,
 
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One can always separate the zeroes first and deal with the rest.
 

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