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why the name “relaxation” in the SOR Gauss-Seidel iterative method?
$begingroup$
The question is that simple. It is in the subject.
Why the name "relaxation" in the SOR Gauss-Seidel iterative method?
I have googled for it without luck.
Moreover, when $omega$ is used in Gauss-Seidel is named "relaxation" and when $omega$ is used in Jacboi is named: "weight" weighted Jacobi method
So, something got to be special about Gauss-Seidel to deserve such a name.
I observed that there is a "relaxation" technique explained in
this thesis back from 1948. I do not see a connection between
relaxation in that context of mechanics (PDEs) and the relaxation asked here which is in the context of linear systems such as Jacobi and Gauss-Seidel.
Hence, I do not consider this as a duplicate questions.
Thanks.
numerical-methods numerical-linear-algebra
asked Jan 30 at 13:43
Herman JaramilloHerman Jaramillo
1,3391019
$endgroup$
add a comment |
$begingroup$
The question is that simple. It is in the subject.
Why the name "relaxation" in the SOR Gauss-Seidel iterative method?
I have googled for it without luck.
Moreover, when $omega$ is used in Gauss-Seidel is named "relaxation" and when $omega$ is used in Jacboi is named: "weight" weighted Jacobi method
So, something got to be special about Gauss-Seidel to deserve such a name.
I observed that there is a "relaxation" technique explained in
this thesis back from 1948. I do not see a connection between
relaxation in that context of mechanics (PDEs) and the relaxation asked here which is in the context of linear systems such as Jacobi and Gauss-Seidel.
Hence, I do not consider this as a duplicate questions.
Thanks.
numerical-methods numerical-linear-algebra
asked Jan 30 at 13:43
Herman JaramilloHerman Jaramillo
1,3391019
$endgroup$
$begingroup$
@Moo : Thanks for your input. I downloaded David Young thesis. Very interesting and helpful. However I scanned through the introduction and could not find why the word "relaxation" is in the SOR abbreviation. Relaxation is a psychological term. What exactly does it have to do with relaxation of an equation? Relaxing what? I do not need to understand what it does (I think I know that). I want to understand where that word came from? Somebody was the first to use that word and it must have an explanation. Thanks.
$endgroup$
– Herman Jaramillo
Jan 30 at 17:39
1
$begingroup$
Possible duplicate of Why some linear iterative methods for linear system are also called "relaxation" methods?
$endgroup$
– Carl Christian
Jan 30 at 20:20
$begingroup$
Maybe because it’s related to functional minimization (energy norm of the error) along the coordinate directions
$endgroup$
– VorKir
Feb 3 at 6:10
add a comment |
$begingroup$
The question is that simple. It is in the subject.
Why the name "relaxation" in the SOR Gauss-Seidel iterative method?
I have googled for it without luck.
Moreover, when $omega$ is used in Gauss-Seidel is named "relaxation" and when $omega$ is used in Jacboi is named: "weight" weighted Jacobi method
So, something got to be special about Gauss-Seidel to deserve such a name.
I observed that there is a "relaxation" technique explained in
this thesis back from 1948. I do not see a connection between
relaxation in that context of mechanics (PDEs) and the relaxation asked here which is in the context of linear systems such as Jacobi and Gauss-Seidel.
Hence, I do not consider this as a duplicate questions.
Thanks.
numerical-methods numerical-linear-algebra
asked Jan 30 at 13:43
Herman JaramilloHerman Jaramillo
1,3391019
$endgroup$
The question is that simple. It is in the subject.
Why the name "relaxation" in the SOR Gauss-Seidel iterative method?
I have googled for it without luck.
Moreover, when $omega$ is used in Gauss-Seidel is named "relaxation" and when $omega$ is used in Jacboi is named: "weight" weighted Jacobi method
So, something got to be special about Gauss-Seidel to deserve such a name.
I observed that there is a "relaxation" technique explained in
this thesis back from 1948. I do not see a connection between
relaxation in that context of mechanics (PDEs) and the relaxation asked here which is in the context of linear systems such as Jacobi and Gauss-Seidel.
Hence, I do not consider this as a duplicate questions.
Thanks.
numerical-methods numerical-linear-algebra
numerical-methods numerical-linear-algebra
asked Jan 30 at 13:43
Herman JaramilloHerman Jaramillo
1,3391019
asked Jan 30 at 13:43
Herman JaramilloHerman Jaramillo
1,3391019
edited Jan 30 at 21:51
Herman Jaramillo
asked Jan 30 at 13:43
Herman JaramilloHerman Jaramillo
1,3391019
asked Jan 30 at 13:43
Herman JaramilloHerman Jaramillo
1,3391019
asked Jan 30 at 13:43
Herman JaramilloHerman Jaramillo
1,3391019
1,3391019
$begingroup$
@Moo : Thanks for your input. I downloaded David Young thesis. Very interesting and helpful. However I scanned through the introduction and could not find why the word "relaxation" is in the SOR abbreviation. Relaxation is a psychological term. What exactly does it have to do with relaxation of an equation? Relaxing what? I do not need to understand what it does (I think I know that). I want to understand where that word came from? Somebody was the first to use that word and it must have an explanation. Thanks.
$endgroup$
– Herman Jaramillo
Jan 30 at 17:39
1
$begingroup$
Possible duplicate of Why some linear iterative methods for linear system are also called "relaxation" methods?
$endgroup$
– Carl Christian
Jan 30 at 20:20
$begingroup$
Maybe because it’s related to functional minimization (energy norm of the error) along the coordinate directions
$endgroup$
– VorKir
Feb 3 at 6:10
add a comment |
$begingroup$
@Moo : Thanks for your input. I downloaded David Young thesis. Very interesting and helpful. However I scanned through the introduction and could not find why the word "relaxation" is in the SOR abbreviation. Relaxation is a psychological term. What exactly does it have to do with relaxation of an equation? Relaxing what? I do not need to understand what it does (I think I know that). I want to understand where that word came from? Somebody was the first to use that word and it must have an explanation. Thanks.
$endgroup$
– Herman Jaramillo
Jan 30 at 17:39
1
$begingroup$
Possible duplicate of Why some linear iterative methods for linear system are also called "relaxation" methods?
$endgroup$
– Carl Christian
Jan 30 at 20:20
$begingroup$
Maybe because it’s related to functional minimization (energy norm of the error) along the coordinate directions
$endgroup$
– VorKir
Feb 3 at 6:10
$begingroup$
@Moo : Thanks for your input. I downloaded David Young thesis. Very interesting and helpful. However I scanned through the introduction and could not find why the word "relaxation" is in the SOR abbreviation. Relaxation is a psychological term. What exactly does it have to do with relaxation of an equation? Relaxing what? I do not need to understand what it does (I think I know that). I want to understand where that word came from? Somebody was the first to use that word and it must have an explanation. Thanks.
$endgroup$
– Herman Jaramillo
Jan 30 at 17:39
$begingroup$
@Moo : Thanks for your input. I downloaded David Young thesis. Very interesting and helpful. However I scanned through the introduction and could not find why the word "relaxation" is in the SOR abbreviation. Relaxation is a psychological term. What exactly does it have to do with relaxation of an equation? Relaxing what? I do not need to understand what it does (I think I know that). I want to understand where that word came from? Somebody was the first to use that word and it must have an explanation. Thanks.
$endgroup$
– Herman Jaramillo
Jan 30 at 17:39
1
1
$begingroup$
Possible duplicate of Why some linear iterative methods for linear system are also called "relaxation" methods?
$endgroup$
– Carl Christian
Jan 30 at 20:20
$begingroup$
Possible duplicate of Why some linear iterative methods for linear system are also called "relaxation" methods?
$endgroup$
– Carl Christian
Jan 30 at 20:20
$begingroup$
Maybe because it’s related to functional minimization (energy norm of the error) along the coordinate directions
$endgroup$
– VorKir
Feb 3 at 6:10
$begingroup$
Maybe because it’s related to functional minimization (energy norm of the error) along the coordinate directions
$endgroup$
– VorKir
Feb 3 at 6:10
add a comment |
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$begingroup$
@Moo : Thanks for your input. I downloaded David Young thesis. Very interesting and helpful. However I scanned through the introduction and could not find why the word "relaxation" is in the SOR abbreviation. Relaxation is a psychological term. What exactly does it have to do with relaxation of an equation? Relaxing what? I do not need to understand what it does (I think I know that). I want to understand where that word came from? Somebody was the first to use that word and it must have an explanation. Thanks.
$endgroup$
– Herman Jaramillo
Jan 30 at 17:39
1
$begingroup$
Possible duplicate of Why some linear iterative methods for linear system are also called "relaxation" methods?
$endgroup$
– Carl Christian
Jan 30 at 20:20
$begingroup$
Maybe because it’s related to functional minimization (energy norm of the error) along the coordinate directions
$endgroup$
– VorKir
Feb 3 at 6:10