Need "impossible" problems

[nbucska]

I am working on a program to find approximate solution
of problems which don't/can't have exact solution e.g.
overdetermined equations, impossible -- as specified -- circuits etc.

I would appreciate such problems to test/refine the SW.


<nbucska@pcperipherals.com>

 

[melone]

Like 1/0? Or PI?

 

[nbucska]

I can give you a few examples. Here are two:

1.) Connecting one to five capacitors parallel to one single resistor realize fifteen different given time constants with minimal error using standard values.

2.) Find the best approximation of an ideal filter characteristics with standard component values.


<nbucska@pcperipherals.com>

 

[m777182]

Maybe I do not understand your problem entirely: overdetermined systems of equations in a simple matrix form Ax=b arise at experimental work and as far as I know we use least squares approach to minimize the sum of the squares of the components of the residual vector.Another approach is the Chebyshev solution.
I believed that connecting one to five capacitors parallel to one single resistor still represent a single time constant where the capacitance is expressed as a sum of partial capacitances, t=R*(C1+C2+...Cn).
Concerning filters I remember the doctoral thesis of my boss at my first employment where he was calculating filters to a very high degree mainly by a hand calulator. If he could do it with a HP35 it should not be a problem with some nowadays machines.Or please, point me out my misunderstanding of the problem.
m777182

 

[nbucska]

77:
These were actual problems solved with the program. It doesn't matter if there is other way or not to solve them.

In both problem using standard component values were serious
complicating factor. The 5 cap can be connected 31 ways.

The point of my posting is : I need difficult problems
I can try to solve to test out/improve/etc. my program.


<nbucska@pcperipherals.com>