20110328, 20:29  #1 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
3·37·41 Posts 
Unusual system of 11 unknowns
I have a series of equations with 11 unknowns (ak)
On the plus side I have many equations ... more than 100. The values of ak are NOT integers. However in each of the equations the resultant(?  the number after the equal sign) is reported as an integer; though is likely isn't an integer. Furthermore, it is now knows whether this resultant is rounded or truncated. Is it possible?, difficult? to solve for a  k? Thanks 
20110328, 21:33  #2  
"Forget I exist"
Jul 2009
Dumbassville
20C0_{16} Posts 
Quote:
however no knowing it's integer allows for approximation only as far as i know( after all the values known are approximate). care to give a list of equations ? maybe then i can help approximate. 

20110328, 22:50  #3 
"William"
May 2003
New Haven
2361_{10} Posts 
That's a lot of equations for only 11 variables  do you have reason to believe there is a simultaneous solution?
I'd try solving it as a minimization problem  the error for each of the equations is the left side minus the right side squared. The total error is the sum of the errors. Use unconstrained minimization methods to search for the smallest error. You might get fancy with the individual error terms to account for truncations or roundoff  I'd try that as a next stage after seeing if the simple approach brought good enough results. 
20110331, 01:18  #4 
Dec 2010
Monticello
5×359 Posts 
You could also try solving the equations 11 at a time and seeing how far apart the lowdimensional (finite number of points) solutions fell.
Of course, I'm assuming your functions are reasonably smooth...otherwise, as in the previous thread on lots of equations, we are going to need some additional information to help us understand the problem. 
20110331, 04:04  #5 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
3×37×41 Posts 
It is a weighted scoring system we use in one of my organizations.
A team is scored in each of the 11 factors and each factor has a "secret" weighting. The scores are whole numbers but the weights may or may not be. Then the final answer is truncated / rounded (I don't know which one). In all the years over 100 teams have been scored. For every team I know the scores they got on each of the 11 factors and the final score as an integer. The scores for each factor have a low of 1 (cannot be 0) and a high somewhere between 5 and 12. The final answer is between 1 and 10. The curious mathematical side of me is interested in knowing if this can be solved. If it helps / matters I am fairly certain that a>=b>=c ,... >=k 
20110331, 04:53  #6 
Aug 2006
1754_{16} Posts 
Ah. In that case I'd go with wblipp's suggestion.

20110331, 04:56  #7  
Jun 2003
2^{3}×607 Posts 
Quote:
1. From the above two statements, I would conclude that the sum of the weights = 1 exactly. 2. If it is a humangenerated system, odds are, the coefficients will be nice round fractions. 

20110331, 21:09  #8  
Dec 2010
Monticello
5·359 Posts 
Quote:


20111211, 22:04  #9 
Sep 2011
6_{8} Posts 
I'm fairly positive this can easily be solved with dynamic programming. Even though the state space is a priori much too large to tackle with explicit enumeration. The number of binding constraints is so large that one can probably dynamically reduce the searching space as the execution of the algorithm goes along.

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Unusual folly  fivemack  Lounge  1  20130425 16:32 
Unusual error  comments George?  PhilF  Software  2  20060426 20:19 
Unusual differentiation  mfgoode  Math  12  20040825 16:33 
unusual sequence  tom11784  Puzzles  5  20040520 12:35 
Unusual Cruncher Deaths...  E_tron  Lounge  6  20031118 23:05 