matrices problem

[Jenny_Louise-di]

hi,





i have posted a question a few weeks ago but i



didn't manage to get an answer... so i have


simplified my main matrice in hope someone can



actually tell me what i am doing wrong now





(the problem is that i don't get the right answer





using the find function)





please help 🙂





thanks


Jen

[TomGutman]

I don't see your problem. The results from find multiply out to values that are very close to zero (around 1e-11 using the L-M algorithm, about 1e-8 using the default linear algorithm). Given the size of the numbers in the matrix, that is quite close, and you cannot really expect anything better.

I have no intention of trying to figure out what the relationship, if any, between the numbers you have at the bottom of the sheet and the original problem posed and solved. As a general rule you should not expect that typing in a whole lot of numbers will be correct -- errors are inevitable when typing, the more you type the more errors you will introduce.
__________________
� � � � Tom Gutman

[Jenny_Louise-di]

(hey i have attached my worksheet again because i
had not realised that mathcad had saved some stuff i
was messing around with.)

thanks tom for the reply but i mean is there really
no way i will end up with 0 as an answer when i
multiply the matrix mat with the 8 unknowns.. is
there any other simple-ish functions i can use
maybe? (i really don't want to sound like a pain but
i have been stressing over this for weeks)

would it make a difference if i calculated it by
hand ( although i dnt think i will be able to do it
but just in case is it worth trying?)

thanks jenny

[TomGutman]

No, you will never get exactly zero. You are doing numeric calculations, using limited precision (IEEE 64 bit format uses a 53 bit mantissa). While the mathematical theory is based on real numbers, which are dense and uncountably infinite in number, the actual numbers you get to use are a finite subset of the rational numbers. There will always be rounding error.

To get exact results you would have to use only integer inputs (no decimal points, fraction values represented as ratios of integers) and then use the symbolic processor. That, in principle, can get you exact results. But ..... the results will be rational numbers (ratios of integers) and the integers can be very long. Commonly too long to be of any practical use, and not infrequently too long for even the symbolic processor to handle.
__________________
� � � � Tom Gutman

[PhilipOakley]

One area to look up is 'condition number'.
This (condition number) tells you how likely small
errors are magnified when solving matrix equations.

There are condition number estimates available in
mathcad. A condition number of 1.00 is 'perfect' (it
can't be less than 1 ;-). The identity matrix has a
condition number of 1 ...

There are whole courses on the fascinating features
of linear algebra, and pages and pages of wikipedia
entries to suck you in deep...

Philip Oakley

[AlvaroDíaz]

Interesting 3 questions for puzzle section:

On 12/8/2009 2:07:23 AM, Tom_Gutman wrote:
>You are doing numeric calculations, using limited precision (IEEE 64 bit format uses a 53 bit mantissa).

>While the mathematical theory is based on real numbers, which are dense and uncountably infinite in number,

For those that maybe don't remember this definitions:

dense set = given two points in the set there are another set point between given points.

countably set = there are a biunivoc correspondence between naturals and set points.

rationals are dense and countably, reals are dense and uncountably and naturals are countably and not dense.

>the actual numbers you get to use are a finite subset of the rational numbers.

It's a finite set, so, first puzzle question: How many numbers mathcad?.

Also, there are more points near zero that in the tails. Second puzzle question: how to make an histogram of the mathcad numbers?

The next puzzle question is evident: which is the stastical distribution for the mathcad numbers?

Regards. Alvaro.

PD: I don't have the answers.

[alnstevens]

On 12/8/2009 2:07:23 AM, Tom_Gutman wrote:
>No, you will never get exactly
>zero...
>There will always be rounding
>error.
_
>� � � � Tom Gutman

Quite right. But, for this problem, you can make the residuals a lot smaller using the symbolic solver - see attached. (Can't see that the solution is any more useful than from the numerical solver though!).

stv

[alnstevens]

On 12/9/2009 10:22:07 AM, stv wrote:

for this problem, you
>can make the residuals a lot smaller
>using the symbolic solver >
>stv

No, on second thoughts it's the scaling factor that does it, not the symbolic solver!

stv

[ptc-1368288]

On 12/7/2009 10:41:37 PM, Jenny_Louise wrote:
>hi,

i have posted a question
>a few weeks ago but i

didn't
>manage to get an answer... so
>i have
simplified my main
>matrice in hope someone can
>

actually tell me what i am
>doing wrong now

(the problem
>is that i don't get the right
>answer
------------------------------
Hard to track the problem back as you have changed thread. It sounds like a pseudo-inverrse problem, which myself and Viktor have done some work on that but your matrice constuct was not sourced and your project couldn't be completed.



using the find
>function)

please help
>:)

thanks
Jen