1

If Gauss-Seidel is more efficient than Jacobi method, then why do we need to learn it? Does it have any advantages over Gauss-Seidel?

sarach
  • 19
  • 1
    The two methods were both useful and widely used in the 1950s. Today however, there exist highly advanced and more efficient methods like the Krylov subspace methods and thus the application of Gauss-Seidel and Jacobi in solving large sparse matrices in our modern days is extremely rare. – SPARSE Oct 15 '21 at 18:28
  • 1
    I am voting to close as opinion based. – Surb Oct 15 '21 at 18:29
  • 1
    @Surb I think the keyword is learn. I interpret the question as: has any pedagogical merit to teach methods that are no longer the state of the art? – Miguel Oct 15 '21 at 18:53
  • 1
    Would probably be more appropriate at math educators stackexchange – kingW3 Oct 15 '21 at 19:18
  • @SPARSE The GROMACS library uses a variant of the nonlinear Gauss-Seidel algorithm to solve nonlinear constraint equations in the context of molecular dynamics. GROMACS has other constraint solvers, but it is safe to say that Gauss-Seidel is still used heavily. – Carl Christian Oct 21 '21 at 09:12
  • @kingW3 Certainly, math.educators is a good option, but answering the question in depth requires specialized knowledge on parallel numerical linear algebra. It is more likely to find this expertise here or at the site for scientific computing. – Carl Christian Oct 21 '21 at 09:17

1 Answers1

3

One of the disadvantages of Gauss-Seidel method is that successive updating of all the entries makes parallelizing this algorithm much harder/inefficient.

Jack Shao
  • 61
  • I fully agree with your assessment. I teach the Jacobi iteration for this reason and I also use it to motivate the study of Krylov subspace methods. – Carl Christian Oct 21 '21 at 09:07