I want to solve for X a cubic equation that contains a vector as an input

Forum|Forum|8 years ago
February 11, 2018
2 replies
5218 views

I am trying to solve a cubic equation for the unknown X, but one of the input parameters is a vector. I tried to solve symbolically and then substitute the vector but something doesn't seem right. Then i tried to program a function that solves it for every value of the vector input, but since the result contains 3 solutions, it doesn't work.

I hope you will be able to find a solution.

Thank you in advance.

P.S. The file is uploaded

1_Problem.rar

Physics

Best answer by Werner_E

The attached sheet should help.

Personally I would prefer the "numerics only" solution at the end as I see no need for using the symbolics.

W

Werner_E

Answer

25-Diamond I

The attached sheet should help.

Personally I would prefer the "numerics only" solution at the end as I see no need for using the symbolics.

1_WE_20180211_Problem_3.zip

D

DrilonShabani

Author

1-Visitor

Perfect solutions. I couldn't find even one.
Thank you very much to you and all others who helped.

L

LucMeekes

23-Emerald IV

Is this what you are after?

(The symbolic result stretches out further to the right)

I prefer a symbolic solution in general, because it can provide more insight...

Success!
Luc

1_LM_20180211_Problem-3.zip

W

Werner_E

25-Diamond I

Hi Luc!

Guess you misunderstood the question. The calculation of a,b,c,d was done somewhat awkward in the OPs sheet, but the question was about the cubic equation which was based on the calculated values of a,b,c,d.

The one with f(eps) and its derivative and with the parameter lambda.

Guess the throughout symbolic solution for this equation will look quite ... interesting 😉

Main question as I understood was how to solve this cubic for a 100 element vector of lambda-values and how to arrange the result in a 3 x 100 matrix.

EDIT

A true symbolic solution could be something shown in the following screenshot. I didn't wait for the calculation to finish and i doubt that the solution (should calculation ever should finish without crashing the program or throwing an error) would provide more insight 😉

EDIT2:

I had Mathcad running while typing this and after sending the post I was confronted with an "out of memory" error. I won't try it in Prime as I think that even though Prime could benefit from the full memory in my machine, and even if Prime could finish this calculation, the result expressions would not be of much help.

Maybe Maple in MC11 has more success, maybe some assumptions like ALL=real or ALL>0 can help.