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Problem of construction of the Gauss-Seidel Mathcad Operator for the solution of a linear systems

Forum|Forum|8 years ago
March 26, 2018
4 replies
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I cannot make to work the algorithm of the attached file containing Gauss-Seidel Operator for linear systems. Can someone give an advice, please? I attached it.

1_gaussseid_r01.zip

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Best answer by Werner_E

Luc's Mathcad 11 (which uses Maple for symbolics) can expand that expression, but Mathcad 15 (and 14) and also Prime use Mupad for symbolics and would refuse to display the result. Don't think that this is due to the symbolic engine but rather a design change in Mathcad itself. Somebody at Mathsoft probably thought that it would be a good idea not to let a symbolic result spread some pages widths - sorry guy, but it was not a good idea.

While MC13 still uses Maple (which is far superior over MuPad) it also had some severe deficits. Thats the reason many consider Mathcad11 as the best version ever. Alas, times go by and from todays point of view its probably MC15 to favor.

F

Fred_Kohlhepp

23-Emerald I

For starters:

The keystroke for a range variable is a semicolon (;) not two periods (..) Mathcad will show two periods, but it won't understand them.
"break" is a programming key word, it cannot be typed.
If you want a literal subscript in a variable (in version 15) you type a decimal (x.old). An array subscript ([) will have Mathcad declaring an undefined variable.
What is this?

T

tubar

Author

1-Visitor

Yes, just on that expression is a problem. I wanted to write inside the Sum operator the below equation but it is impossible because appears automatically a void space before "if" that i dont understand why.

equation of iteration.png

W

Werner_E

25-Diamond I

On point, additionally to what Fred had already said:

When taking the absolute value of a variable or an expression, Mathcad often can't know if you really mean the absolute value or if you want to take the determinant of a square matrix.

Rightclick at your absolute values and tell Mathcad what your intention is:

Concerning your confusion about the "if".

Mathcad offers two of them.

One is the programming if-statement which you chose via the programming palette or its keyboard short cut.

The second is the if-function,

The latter is what you want to use here. this time you simple type "if" and don't chose from the palette.

Nevertheless - when I correct all those errors, i ran into a divison by zero error. You may want to look over it again.

T

tubar

Author

1-Visitor

Yes, typing directly the command "if" it is allowed the trick. But the issue remains unsolved as we still dont have the solution through Gauss-Seidel Method.

W

Werner_E

25-Diamond I

It looks like you are just retyping a program from a print of a Mathcad sheet.

So check your sheet for typos and keep in mind that there is a big difference between vector indices and literal indices (as you would use for x.old).

L

LucMeekes

23-Emerald IV

I suppose you're not interested in the simple solution: let Mathcad do the work.

Some usage examples:

Success!
Luc

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-MFra-

21-Topaz II

I have adapted the program to the case of any origin. It is known that convergence occurs with dominant diagonal matrices and for symmetric and positive definite matrices.

3_GSS.zip

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Werner_E

25-Diamond I

This new approach suffers from the same problem as the OPs variant.

The algorithm works if the diagonal elements are large and it works guaranteed if the matrix is diagonally dominant like your second example. Unfortunately its not always possible to rearrange the rows or columns easily in such a way that the matrix would be suitable for this algorithm.

And Applying more work in changing the system/matrix would mean a similar effort than solving the system exactly via Gauß or similar.