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HP Forum Archive 17

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Iteration on 33s or 35s?
Message #1 Posted by Howard Boardman on 29 Oct 2007, 8:08 p.m.

Is it possible to use iteration to solve an equation with the 33s or 35s? For examply if you have 3 varibles in an equation (such as a polynomial) where there are multiple roots possible, and you know 2 of the variables and need to solve for the 3rd. The solver often returns the incorrect root, although it is mathematically correct. I've run into this with a few civil engineering problems. What I'd like to do is have a root returned and see if it returns the correct solution for the other variables and can iterate a solution until the correct result is obtained for all variables. Thanks for any info.

      
Re: Iteration on 33s or 35s?
Message #2 Posted by Karl Schneider on 30 Oct 2007, 12:46 a.m.,
in response to message #1 by Howard Boardman

Howard --

It sounds as though you are melding two different things:

  • Polynomials having an order n and one variable for n possible roots (solutions)

  • Multi-variable equations

However, I'm fairly sure that I know the gist of your question: You're wondering why you always get the same result when solving for the only unspecified variable, which appears only once in the equation.

The answer is that the HP-33s and HP-35s will provide a "direct solution" determined by internal algebraic methods, in cases where it deems possible. They will ignore your two initial guesses to provide this direct solution. This flawed logic was borrowed from the solver in the HP-19B/II and HP-27S.

The workaround is to add a mathematically inert term such as "+0*X" to the equation in order to trick the calculator into concluding that the equation is algebraically intractable. Then, it will use numerical iteration with your initial guesses.

An archived thread and an article:

http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv014.cgi?read=62608#62608

HP SOLVE-INTEG on all RPN-based models

As for the last part of your query: There may be an infinite number of solutions for a single multi-variable equation. Solution for multi-input, multi-output systems of equations is not supported by the HP-33s or HP-35s. An HP-50g can be used for that purpose.

-- KS

Edited: 30 Oct 2007, 1:27 a.m. after one or more responses were posted

            
Re: Iteration on 33s or 35s?
Message #3 Posted by Howard Boardman on 30 Oct 2007, 1:10 a.m.,
in response to message #2 by Karl Schneider

Karl-

Very good point. I think you answered my question. I will give it a try. As much of an engineer I like to think I am, I am not a mathematician. I can only love math so far as it solves my problems :) Thanks for straightening out my logic. As many complaints as there are heard about the 33s and the like, they are very powerful little beasts. The ability to solve for any variable on the fly in an equation is something I wish I had known about in college.

                  
Re: Iteration on 33s or 35s?
Message #4 Posted by Martin Pinckney on 30 Oct 2007, 2:20 p.m.,
in response to message #3 by Howard Boardman

Quote:
The ability to solve for any variable on the fly in an equation is something I wish I had known about in college.

Well, I've been out of college a long time (since slide rule days), but I agree about the Equation Solver, it's the best feature any calculator can have! Who needs keystroke programming?

                        
Re: Iteration on 33s or 35s?
Message #5 Posted by Don Shepherd on 30 Oct 2007, 4:14 p.m.,
in response to message #4 by Martin Pinckney

Quote:
Who needs keystroke programming?
I do!
                              
Re: Iteration on 33s or 35s?
Message #6 Posted by Martin Pinckney on 30 Oct 2007, 10:14 p.m.,
in response to message #5 by Don Shepherd

I used to do keystroke programming a lot back in the early 1980's, when I had a TI-59. Then along came personal computers, and calculator programming went out the window...

Someday soon I am going to re-teach myself to do programming, this time on my 35s... and incorporate equations into the programs.


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