If Ax = Ax, then XTAX =xT(Ax) = MXTX), and the Rayleigh quotient, R(x) =.x'Axequals A. If x is close to an eigenvector for , then this quotientclose to A. When A is a symmetric matrix (AT = A), the Rayleigh quotient R(x) =A =5 9will have roughly twice asx'xmany digits of accuracy as the scaling factor , in the power method. Compute H, and R(x,) for k = 1, ., 4.Complete the table below using the power method.k234(Round to four decimal places as needed.)

See step 2 for solution by power method.

x'Ax , equals A. If x is close to an eigenvector for 2, then this quotient is close to A. When A is a symmetric matrix (AT = A), the Rayleigh quotient R(x,) = x'x If Ax = ix, then XTAX = x"(Ax) = (xTx), and the Rayleigh quotient, R(x) = will have roughly twice as AD many digits of accuracy as the scaling factor H, in the power method. Compute H, and R(x,) for k= 1, ., 4. Complete the table below using the power method. k (Round to four decimal places as needed.)

x'Ax , equals A. If x is close to an eigenvector for 2, then this quotient is close to A. When A is a symmetric matrix (AT = A), the Rayleigh quotient R(x,) = x'x If Ax = ix, then XTAX = x"(Ax) = (xTx), and the Rayleigh quotient, R(x) = will have roughly twice as AD many digits of accuracy as the scaling factor H, in the power method. Compute H, and R(x,) for k= 1, ., 4. Complete the table below using the power method. k (Round to four decimal places as needed.)

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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Question

If Ax = Ax, then XTAX =xT(Ax) = MXTX), and the Rayleigh quotient, R(x) =.
x'Ax
equals A. If x is close to an eigenvector for , then this quotient
close to A. When A is a symmetric matrix (AT = A), the Rayleigh quotient R(x) =
A =
5 9
will have roughly twice as
x'x
many digits of accuracy as the scaling factor , in the power method. Compute H, and R(x,) for k = 1, ., 4.
Complete the table below using the power method.
k
2
3
4
(Round to four decimal places as needed.)

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