Question

Consider the following system of non-linear equations describing the intersection of 3 ellipsoids to be solved using Newton's method:

5184x²+81(y-3)²+16(z+9)² = 1296
144x²+9(y-5)²+(+6)² = 144
2304(x+0.5)²+81(y-5)²+576z² = 5184
Code a function fp4 that takes as input the 3 entry column vector x and provides as output the 3 entry column vector f associated with the above system of non-linear equations evaluated at x.

Answer 1

To solve the given system of non-linear equations, you can code a function that evaluates the equations at a given input vector x.

Step-by-step explanation:

To code a function fp4 that takes as input the 3 entry column vector x and provides as output the 3 entry column vector f associated with the given system of non-linear equations, we need to evaluate the equations at x. Let's start by rewriting the given equations:

5184x²+81(y-3)²+16(z+9)² = 0

1296144x²+9(y-5)²+(+6)² = 0

1442304(x+0.5)²+81(y-5)²+576z² = 0

The function fp4 will take a 3 entry column vector x as input and compute the corresponding column vector f by substituting the values of x into the equations. The resulting vectors will represent the system of non-linear equations evaluated at x.