Question

Write a program to solve the system of nonlinear equations using Newton's method: • 1 = $x^4 + y^4$ • 0 = $x^3 - y$ Run Newton's method for 5 iterations, and save the result of each iteration in `guesses`. As a starting guess, take each variable to be 1. In the starter code, you are provided the function `f` that represents the system of nonlinear equations, as well as the array `w` that should serve as your initial guess. Your code snippet should define the following variables: Name Type Description `guesses` 2D numpy array A numpy array of shape 5 × 2, where `guesses[i]` is the ($i$ + 1)th guess from Newton's method user_code.py 1 import numpy as np 2 import numpy.linalg as la 3 4 def f(w): 5 x, y = w 6 return np.array([ 7 x4 + y4 - 1, 8 x**3 - y]) 9 10 guesses = np.zeros((5,2)) 11 12 # Initial guess, don't save this in output 13 w = np.array([1.,1.])

          Write a program to solve the system of nonlinear equations using Newton's method:
• 1 = $x^4 + y^4$
• 0 = $x^3 - y$
Run Newton's method for 5 iterations, and save the result of each iteration in `guesses`. As a starting guess, take each variable to be 1.
In the starter code, you are provided the function `f` that represents the system of nonlinear equations, as well as the array `w` that should serve as your initial guess.
Your code snippet should define the following variables:
Name	Type	Description
`guesses`	2D numpy array	A numpy array of shape 5 × 2, where `guesses[i]` is the ($i$ + 1)th guess from Newton's method
user_code.py
1 import numpy as np
2 import numpy.linalg as la
3
4 def f(w):
5	x, y = w
6	return np.array([
7		x**4 + y**4 - 1,
8		x**3 - y])
9
10 guesses = np.zeros((5,2))
11
12 # Initial guess, don't save this in output
13 w = np.array([1.,1.])

Write a program to solve the system of nonlinear equations using Newton's method:
• 1 = x^4 + y^4
• 0 = x^3 - y
Run Newton's method for 5 iterations, and save the result of each iteration in `guesses`. As a starting guess, take each variable to be 1.
In the starter code, you are provided the function `f` that represents the system of nonlinear equations, as well as the array `w` that should serve as your initial guess.
Your code snippet should define the following variables:
Name Type Description
`guesses` 2D numpy array A numpy array of shape 5 × 2, where `guesses[i]` is the (i + 1)th guess from Newton's method
usercode.py
1 import numpy as np
2 import numpy.linalg as la
3
4 def f(w):
5 x, y = w
6 return np.array([
7 x**4 + y**4 - 1,
8 x**3 - y])
9
10 guesses = np.zeros((5,2))
11
12 # Initial guess, don't save this in output
13 w = np.array([1.,1.])

Added by Jeremy B.

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