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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
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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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.)
Transcribed Image Text: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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