Suppose we have data = = k=1,...,m and corresponding values y [k]k=1, and we want to find a polynomial pr(x) = Σ}_ª¡z³ which is the "best fit" for the given data. We can find such polynomial by finding coefficients {a} that minimizes the sum j=0 m K = [yk - Pn(x)]². k=1 The partial derivatives of K with respect to the coefficients of p, must be zero, i.e. for i = 0,...,n, data Day Temperature 1 87 2 80.3 3 83.3 n m m 4 87.1 m әк 0 2Σ - P(x)] Σα; Σ i+j X k = хкук (1) 5 89.7 Dai k=1 j=0 k=1 k=1 6 90.1 7 82.3 import numpy as np Here, we have the convention that x = 1. Let 8 79.2 def vander(x, degree): 9 65.5 V = [z{\i=1___m_j=0,..., and a = [ai]=0..... 10 64.4 m = len(x) Then system (1) is equivalent to VTVa = VTy. The solution to this gives the coefficient of the polynomial which is the "best fit" for the given data. Find the coefficients of polynomial with degree 3 using QR factorization which is the best fit" for the data. Compute for the value of K. 12215676222 59.8 n-degree +1 60.2 V= np.zeros((m, n)) 13 65.5 14 71.2 for i in range(m): 77.1 for j in range(n): 73.9 69.1 V[i, j] = x[ü] **j 18 58.4 19 63.8 return V 20 73.5 51.1
Suppose we have data = = k=1,...,m and corresponding values y [k]k=1, and we want to find a polynomial pr(x) = Σ}_ª¡z³ which is the "best fit" for the given data. We can find such polynomial by finding coefficients {a} that minimizes the sum j=0 m K = [yk - Pn(x)]². k=1 The partial derivatives of K with respect to the coefficients of p, must be zero, i.e. for i = 0,...,n, data Day Temperature 1 87 2 80.3 3 83.3 n m m 4 87.1 m әк 0 2Σ - P(x)] Σα; Σ i+j X k = хкук (1) 5 89.7 Dai k=1 j=0 k=1 k=1 6 90.1 7 82.3 import numpy as np Here, we have the convention that x = 1. Let 8 79.2 def vander(x, degree): 9 65.5 V = [z{\i=1___m_j=0,..., and a = [ai]=0..... 10 64.4 m = len(x) Then system (1) is equivalent to VTVa = VTy. The solution to this gives the coefficient of the polynomial which is the "best fit" for the given data. Find the coefficients of polynomial with degree 3 using QR factorization which is the best fit" for the data. Compute for the value of K. 12215676222 59.8 n-degree +1 60.2 V= np.zeros((m, n)) 13 65.5 14 71.2 for i in range(m): 77.1 for j in range(n): 73.9 69.1 V[i, j] = x[ü] **j 18 58.4 19 63.8 return V 20 73.5 51.1
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make a python code
![Suppose we have data =
=
k=1,...,m
and corresponding values y [k]k=1, and we want to
find a polynomial pr(x) = Σ}_ª¡z³ which is the "best fit" for the given data. We can find such
polynomial by finding coefficients {a} that minimizes the sum
j=0
m
K = [yk - Pn(x)]².
k=1
The partial derivatives of K with respect to the coefficients of p, must be zero, i.e. for i = 0,...,n,
data
Day
Temperature
1
87
2
80.3
3
83.3
n
m
m
4
87.1
m
әк
0
2Σ - P(x)]
Σα; Σ
i+j
X k
=
хкук
(1)
5
89.7
Dai
k=1
j=0
k=1
k=1
6
90.1
7
82.3
import numpy as np
Here, we have the convention that x = 1. Let
8
79.2
def vander(x, degree):
9
65.5
V = [z{\i=1___m_j=0,...,
and
a = [ai]=0.....
10
64.4
m = len(x)
Then system (1) is equivalent to VTVa = VTy. The solution to this gives the coefficient of the
polynomial which is the "best fit" for the given data.
Find the coefficients of polynomial with degree 3 using QR factorization which is the
best fit" for the data. Compute for the value of K.
12215676222
59.8
n-degree +1
60.2
V= np.zeros((m, n))
13
65.5
14
71.2
for i in range(m):
77.1
for j in range(n):
73.9
69.1
V[i, j] = x[ü] **j
18
58.4
19
63.8
return V
20
73.5
51.1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6492380a-9bea-4212-bceb-c2d87a533728%2F76fa089a-db7b-4fa1-809d-e7640bb79ff1%2F299bcsm_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose we have data =
=
k=1,...,m
and corresponding values y [k]k=1, and we want to
find a polynomial pr(x) = Σ}_ª¡z³ which is the "best fit" for the given data. We can find such
polynomial by finding coefficients {a} that minimizes the sum
j=0
m
K = [yk - Pn(x)]².
k=1
The partial derivatives of K with respect to the coefficients of p, must be zero, i.e. for i = 0,...,n,
data
Day
Temperature
1
87
2
80.3
3
83.3
n
m
m
4
87.1
m
әк
0
2Σ - P(x)]
Σα; Σ
i+j
X k
=
хкук
(1)
5
89.7
Dai
k=1
j=0
k=1
k=1
6
90.1
7
82.3
import numpy as np
Here, we have the convention that x = 1. Let
8
79.2
def vander(x, degree):
9
65.5
V = [z{\i=1___m_j=0,...,
and
a = [ai]=0.....
10
64.4
m = len(x)
Then system (1) is equivalent to VTVa = VTy. The solution to this gives the coefficient of the
polynomial which is the "best fit" for the given data.
Find the coefficients of polynomial with degree 3 using QR factorization which is the
best fit" for the data. Compute for the value of K.
12215676222
59.8
n-degree +1
60.2
V= np.zeros((m, n))
13
65.5
14
71.2
for i in range(m):
77.1
for j in range(n):
73.9
69.1
V[i, j] = x[ü] **j
18
58.4
19
63.8
return V
20
73.5
51.1
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