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Bill Choi

Hong Kong
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Posted - 10/12/2006 :  01:07:01 AM  Show Profile  Edit Topic  Reply with Quote  View user's IP address  Delete Topic
Dear all,

I'm looking for the solution of a cubic equation, which is required in my non-linear square fitting. Is there any reliable sources or websites that contains these mathematical equations, formulas, and solutions? Thank you very much!


Bill CHOI

erica-cn

China
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Posted - 10/12/2006 :  01:51:35 AM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Hi C. F. Choi

Would you please attach your formula and tell us what you want to get?

Thank you

Erica Shang
OriginLab Technical Service
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Bill Choi

Hong Kong
Posts
Posted - 10/12/2006 :  05:53:45 AM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Hi Erica,

The equation is:

C(total) = Cm+2*K1*Cm^2+3*K1*K2*Cm3

I need the solution of this cubic equation in Cm. The value of Cm is further used in the fitting by varying K1 and K2. Although the solution of this equation is given in the literature, I cannot get the satisfactory result (The solution of this equation from the literature is attached). Moreover, it is discouraging that there's no reference about the derivation of this solution.

In addition, I found this solution use almost the same definitions (eg. D, Q, R) as found on the mathematic web site (http://mathworld.wolfram.com/CubicFormula.html), but some of the function is different (arctan instead of arccos and also the term Q/W). Therefore I need some reliable sources to verify the solution quoted in the reference is correct or not.

Thanks!
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larry_lan

China
Posts
Posted - 10/12/2006 :  10:27:40 PM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Hi Bill:

I have no anymore idea to solve the equation, maybe you can try some other packages like MatLab or Mathematica to do the symbolic computation.

Larry
OriginLab Technical Services
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Mike Buess

USA
3037 Posts
Posted - 10/13/2006 :  07:37:14 AM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Hi Bill,

I've used the exact solution from the math tables in CRC Handbook of Chemistry & Physics with success. I trust Wolfram's solution as well although both solutions are complicated enough that I don't want to compare them. Point is, the solution to the cubic equation is well documented if not well known.

Mike Buess
Origin WebRing Member
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