95 XTAX If Ax=xx, then x Ax = x (2x)=2(xx), and the Rayleigh quotient, R(x) = 1 equals. If x is close to an eigenvector for λ, then this quotient is close to λ. When A is a symmetric matrix (AT =A), the Rayleigh quotient A= 59 x'x T xK+ хо R(x)= will have roughly twice as many digits of accuracy as the scaling factor μ in the power method. Compute μ and R(x) for k = 1, ..., 4.

95 XTAX If Ax=xx, then x Ax = x (2x)=2(xx), and the Rayleigh quotient, R(x) = 1 equals. If x is close to an eigenvector for λ, then this quotient is close to λ. When A is a symmetric matrix (AT =A), the Rayleigh quotient A= 59 x'x T xK+ хо R(x)= will have roughly twice as many digits of accuracy as the scaling factor μ in the power method. Compute μ and R(x) for k = 1, ..., 4.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.3: The Gram-schmidt Process And The Qr Factorization

Problem 1BEXP

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