The calculator

[dedndave]

i sometimes "add" equations, which is what you are essentially doing with the matricies

[RuiLoureiro]

i sometimes "add" equations, which is what you are essentially doing with the matricies

or multiply by c and add.
               But the calculator cannot solve 2 systems
               only 1 system at a time. All parameters in one system
               are real constants not variables.

[Gunther]

Hi Rui,

        I think this is what you call
        an ill conditioned linear equation system:
        a linear equation system that depends on one or more
        parameters.

no, not really. If you would draw both equations of system A into a coordinate system, you would see a clear intersection of both lines. That's our solution. The situation is total different with system B. You would see that both lines are smeared. That's the bad condition. Both equations are linear independent, but both are almost parallel.

Gunther

[RuiLoureiro]

Gunther,
        I don't know what you want the calculator should do.
       
When we type the following system B:
(a)   x +    2y = 3
(b)  2x +  4.1y = 4

the calculator should give a pair of values for which
(a) and (b) are true. And this is exactly what i want.
The calculator doesn't study each coefficient or any relationship
between each equation. The calculator will never do this.
If we want to study the relationship between (a) and (b)
its another question you should solve.
The calculator doesn't do any geometric interpretation also
and will never do it.
If the angle between (a) and (b) are too small or too too small or not, the calculator does not compute it. It computes only the solution of the system.

So, the calculator will give only the solution: x = 43 and y = -20.
and the answer to your question

Did you test some ill conditioned equation systems?

seems to be this: no and never (if i understood whats behind it).

[Gunther]

Rui,

So, the calculator will give only the solution: x = 43 and y = -20.

no offense, my posts wasn't meant as criticism. The Calculator brings the right result and that shows that it is numerically stable. :t The point with the coordinate system was only included to illustrate what's behind the term "ill conditioned". It's clear that the Calculator won't draw the system; that wouldn't be necessary and is in the most cases impossible. I apologize for the misunderstanding.

Gunther   

[RuiLoureiro]

Gunther,

         «no offense, my posts wasn't meant as criticism.»

         I didnt get it in that way.  No problems :t

         About the calculator, i wrote what i wrote
         and i know what i want to do or if i want to
         do something more ! In this particular case
         of solving linear equation systems of 2,3,4
         unknowns i don't want to know if the angle
         between (a) and (b), (b) and (c) etc.
         are so small or so so small or not. To me
         it is irrelevant when the calculator
         wants to solve linear equation systems of 2,3,4
         unknowns. Only this.

[RuiLoureiro]

Gunther,
        I was working about complex functions
        to be used in my "the calculator",
        when you asked me for something that has
        something to do with
        "an ill conditioned linear equation system".
        I used the calculator to see if there was
        any problem when we try to solve a system.
        And there was and i corrected the problem.
        Meanwhile, my problem was to know
        what you call a "an ill conditioned...",
        thing that i never heard. But it is also
        true that i don't follow this kind of
        things there are many years. It could be
        seen as a concept, but i don't give
        importance to be included in the calculator.
        Now, it seems we know what is the question
        and, for me, it is solved. You give importance
        and i think that it is out of context for
        what i want the calculator should do.
        I want to say that it seems that you have
        a good background about this things...
        The way you set the question, the way you
        wrote about it, ... Nothing more to say.
        I hope you give the best interpretation
        to my replies.
        I hope you recover soon as possible.  :t

[Gunther]

Hi Rui,

        I hope you recover soon as possible.  :t

thank you for the good wishes. The cold is very persistent.

        I hope you give the best interpretation
        to my replies.

Yes of course. I think you've made a good job with the Calculator.  :t

Gunther

[RuiLoureiro]

Hi Gunther,
                  take the correct tablets and wait ! :t

[RuiLoureiro]

Dave,
        What do you call "a possibly more complex system" ?
       
        Don't forget that we are talking about "linear equation systems".
        And to be solved by a computer procedure.       

        It seems that there are "linear equation systems" and
           "linear complex equation systems"
        or "complex linear equation systems"
        or "linear equation complex systems" (don't know)
        Where did you see it, Dave? 

[dedndave]

you can always make a line formula more complex
for example, one of the constants may be the sin(angle) - something like that
at a specific angle, the function is linear, but changes as the angle changes

you could also introduce time into the equation
at any given moment, the function is linear - and may be evaluated as such
but, the constants change with time

[dedndave]

the reason i bring it up is....

let's say i evaluate a linear equation in a loop
at each pass - constants
but - the constants are different for different passes

the evaluation process should be able to handle any set of input values

[Gunther]

Dave,

Rui's question is justified.

you can always make a line formula more complex
for example, one of the constants may be the sin(angle) - something like that

No, that wouldn't be a linear equation system, because the sine is bent. You're talking about a non-linear equation system. That's not so easy to solve and most of these systems can only be solved approximately. That's another point.

Gunther

[RuiLoureiro]

you can always make a line formula more complex
for example, one of the constants may be the sin(angle) - something like that
at a specific angle, the function is linear, but changes as the angle changes

you could also introduce time into the equation
at any given moment, the function is linear - and may be evaluated as such
but, the constants change with time

Ok Dave,
        now, i understood the idea.
        Yes, if the constants are real
        the system is a linear equation system.

        The system is non-linear in x if we use sin(x) instead of x
         or x^2, e^x, ...

        For instance:  2 sin(3t) x+  y=5
                               2 x- 3y=10       for t={...}
--------------------------------------------------------------------
        For each t, we get a real number A=2*sin(3t),
        we have a linear equation system,
        we may solve it, we may have or not a solution,
        etc. etc.
---------------------------------------------------------------------
        But this:     2 sin(3x)+  y=5
                            2 x- 3y=10

        is a non-linear equation system.       
   

[dedndave]

Gunther....
sin(45) is a constant   :P