Method to solve the following system of nonlinear equations? 141,3829=A+B/323+5,78C+F323^E 69,07645=A+B/333+5,81C+F333^E 40,55085=A+B/343+5,84C+F343^E 27,92544=A+B/353+5,87C+F353^E 19,7697=A+B/363+5,89C+F363^E where A,B,C,E,F are needs to be determined

tamola7f

tamola7f

Answered question

2022-09-10

Method to solve the following system of nonlinear equations?
141 , 3829 = A + B 323 + 5 , 78 C + F 323 E 69 , 07645 = A + B 333 + 5 , 81 C + F 333 E 40 , 55085 = A + B 343 + 5 , 84 C + F 343 E 27 , 92544 = A + B 353 + 5 , 87 C + F 353 E 19 , 7697 = A + B 363 + 5 , 89 C + F 363 E
where A , B , C , E , F are needs to be determined

Answer & Explanation

Grace Moses

Grace Moses

Beginner2022-09-11Added 13 answers

One approach is to use Newton's method for solving F ( x ) = 0.
Given an approximate solution x i , we would ideally like to find Δ x so that F ( x i + Δ x ) = 0. That's too difficult though, so instead, we use the approximation
F ( x i + Δ x ) F ( x i ) + F ( x i ) Δ x ,
F ( x i + Δ x ) F ( x i ) + F ( x i ) Δ x ,
and we choose Δ x i so that the right hand side is equal to 0. Note that F ( x i ) is a matrix.
We then set x i + 1 = x i + Δ x. We then improve x i + 1 , etc.

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