Let A be the 10 × n matrix formed by the first n columns of the 10 × 10 Hubert matrix. Let c be the n- vector (1,... 1], and set b = A c . Use the normal equations to solve the least squares problem for (a) n = 6 (b) n = 8 , and compare with the correct least squares solution x ¯ = c . How many correct decimal places can be computed? Use condition number to explain the results. (This least squares problem is revisited in Computer Problem 4.3.7 .)
Let A be the 10 × n matrix formed by the first n columns of the 10 × 10 Hubert matrix. Let c be the n- vector (1,... 1], and set b = A c . Use the normal equations to solve the least squares problem for (a) n = 6 (b) n = 8 , and compare with the correct least squares solution x ¯ = c . How many correct decimal places can be computed? Use condition number to explain the results. (This least squares problem is revisited in Computer Problem 4.3.7 .)
Solution Summary: The author explains how to use the normal equations to solve the least squares problem Ax=b for n=6.
Let A be the
10
×
n
matrix formed by the first n columns of the
10
×
10
Hubert matrix. Let c be the n-vector (1,... 1], and set
b
=
A
c
. Use the normal equations to solve the least squares problem for (a)
n
=
6
(b)
n
=
8
, and compare with the correct least squares solution
x
¯
=
c
. How many correct decimal places can be computed? Use condition number to explain the results. (This least squares problem is revisited in Computer Problem 4.3.7 .)
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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