4
$\begingroup$

Iterative methods, like Jabobi method or Gauss-Seidel method, are also called relaxation methods. I understand these methods converge to the true solution in under some condition, but I don't understand why it is "relaxation".

Could someone help explain what does this "relaxation" mean and in what way it is "relaxed"? And what are "non-relaxed" methods for solving linear system?

PS: I am familiar with the relation in optimization, in which the constraint is relaxed to a larger set to make the problem easier to solve.

$\endgroup$

1 Answer 1

Reset to default
2
$\begingroup$

The use of "relaxation methods" where promoted by R. V. Southwell, see this review

https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/relaxation-methods-in-theoretical-physics-volume-11-by-r-v-southwell-oxford-clarendon-press-1956-274-pp-55s/AB8B0D6671801DB050573B26DAFB2DDA

The origin of the term (engineering, allowing joints to move, i.e. relax them) is explained in Chapter 1 of this 1949 master thesis

http://arizona.openrepository.com/arizona/bitstream/10150/319608/1/AZU_TD_BOX90_E9791_1949_40.pdf

$\endgroup$
1
  • $\begingroup$ Very interesting what you are saying here. Still I do not see well the connection between relaxation methods in mechanics (differential equations) and the Jacobi and Gauss-Seidel method. Indeed the Laplace equation in finite differences produce some linear system but that alone does not let me see the Jacobi and Gauss-Seidel as a relaxation method. Thanks. $\endgroup$
    – Herman Jaramillo
    Commented Jan 30, 2019 at 21:44

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .