Hi,
From the information provided, I recognize that the provided vector is a polynomial expression in terms of c3, c2, and c1, and you want to calculate the exact values of c3, c2, and c1.
To determine the exact values of c3, c2, and c1, you would need to solve these polynomial equations equating each to 0. However, the degree of the polynomial in each variable is quite high, making it computationally challenging to find the exact solutions using standard algebraic methods.
One approach to this problem would be utilizing numerical methods, such as polynomial root-finding algorithms. These algorithms can approximate the roots of a polynomial equation with high precision, even for high-degree polynomials. Some popular root-finding algorithms include:
- Newton's Method
- Bisection Method.
You can use one of the mentioned methods to find c3 from the third equation and then substitute it in the first and second equations to calculate c1 and c2 similarly.
Please refer to the following links to know more about Newton's method and the Bisection Method:
- https://orionquest.github.io/Numacom/newton.html
- https://orionquest.github.io/Numacom/bisection.html
It is important to note that these methods can be efficient for large coefficients but may not provide the exact solution.
I hope it helps.
