Consider the data and the initial point ^= ( ²₁ ₂²) A 2 x(0) = and b = = (8). How long does it take Jacobi's method to reduce the absolute max-norm error to a value less than 1/2? In other words, what is the smallest kEN such that the k-th iterate x(k) of Jacobi's method satisfies where x*=(3,5)T is the unique solution of the problem Ax=b? ||x(k) - x* ||∞ ≤ < 1/1/1 O a. Jacobi's method does not converge in this example, and the stopping criterion (*) is not satisfied for any KEN. O b. k=0, i.e. the stopping criterion (*) is already satisfied by the initial point x(0) O c. k=1 O d. k=2 O e. k=4 O f. k=8 O g. k=16 Oh. k=32
Consider the data and the initial point ^= ( ²₁ ₂²) A 2 x(0) = and b = = (8). How long does it take Jacobi's method to reduce the absolute max-norm error to a value less than 1/2? In other words, what is the smallest kEN such that the k-th iterate x(k) of Jacobi's method satisfies where x*=(3,5)T is the unique solution of the problem Ax=b? ||x(k) - x* ||∞ ≤ < 1/1/1 O a. Jacobi's method does not converge in this example, and the stopping criterion (*) is not satisfied for any KEN. O b. k=0, i.e. the stopping criterion (*) is already satisfied by the initial point x(0) O c. k=1 O d. k=2 O e. k=4 O f. k=8 O g. k=16 Oh. k=32
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the data
and the initial point
O d. k=2
4-(²-2)
A =
where x*=(3,5) is the unique solution of the problem Ax=b?
O e. k=4
How long does it take Jacobi's method to reduce the absolute max-norm error to a value less than 1/2? In other words, what is the
smallest KEN such that the k-th iterate x(k) of Jacobi's method satisfies
O f. k=8
g. k=16
** - (8)
=
Oh. k=32
and
|| x(k) x* ||∞ ≤
· (²).
1
2²
a. Jacobi's method does not converge in this example, and the stopping criterion (*) is not satisfied for any KEN.
O b. k=0, i.e. the stopping criterion (*) is already satisfied by the initial point x(0)
O c. k=1
b =
(*)
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