Advantages of guass elimination method
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What are the pros and cons of Gaussian elimination?
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Victor Eijkhout, Mathematician, musician, all-round renaissance man.
Updated May 12
Mathematical algorithms are usually not described in terms of pro and con. But let’s see if we can make sense of this question.
What do you use Gaussian Elimination for? Solving a linear system. How else could you solve a linear system?
You could compute the inverse and multiply with that. You can compute the inverse in (at least) two ways: with Gaussian elimination (more precisely: the Gauss-Jordan algorithm), or Kramer’s rule. The latter is very expensive and probably unstable. But if you already already have the LU factorization from Gaussian elimination, you might as well use that, rather than first compute the inverse, not?
More interesting is that you can use an iterative method for solving the linear system. In that case GE has the pro of being guaranteed to work (up to roundoff), while iterative methods can fail, or use an unpredictable amount of time. GE has the disadvantage in the practical case of sparse matrices that it needs way more memory, and potentially more time.
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1 ANSWER

Victor Eijkhout, Mathematician, musician, all-round renaissance man.
Updated May 12
Mathematical algorithms are usually not described in terms of pro and con. But let’s see if we can make sense of this question.
What do you use Gaussian Elimination for? Solving a linear system. How else could you solve a linear system?
You could compute the inverse and multiply with that. You can compute the inverse in (at least) two ways: with Gaussian elimination (more precisely: the Gauss-Jordan algorithm), or Kramer’s rule. The latter is very expensive and probably unstable. But if you already already have the LU factorization from Gaussian elimination, you might as well use that, rather than first compute the inverse, not?
More interesting is that you can use an iterative method for solving the linear system. In that case GE has the pro of being guaranteed to work (up to roundoff), while iterative methods can fail, or use an unpredictable amount of time. GE has the disadvantage in the practical case of sparse matrices that it needs way more memory, and potentially more time.
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