Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 12.1, Problem 8E
a.
To determine
To find: The Eigen value to which the inverse power iteration with the given shift s will converge and determine convergence rate constant.
b.
To determine
To find: The Eigen value to which the inverse power iteration with the given shift s will converge and determine convergence rate constant.
c.
To determine
To find: The Eigen value to which the inverse power iteration with the given shift s will converge and determine convergence rate constant.
d.
To determine
To find: The Eigen value to which the inverse power iteration with the given shift s will converge and determine convergence rate constant.
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Students have asked these similar questions
Suppose the 3 x 3 matrix A has eigenvalues A₁ = -6, A₂ = -2, and A3 = 5.
(a) Let u be randomly chosen vector in R³. Set
and for k> 0 set
xo
V
||v||'
Xo = xo Axo
Ark
Fk+1 =
Xk+1
||Axk||¹
i. What number do you expect A to converge to?
1¹Axk+1
=Xk+1
ii. What number do you expect ||Ark - A|| to converge to?
iii. For large k, æ, is approximately an eigenvector corresponding to which eigenvalue of A?
(1)
(2)
find the eigenvalues 3*3 matrix
(-1 4 -2
-3 4 0
-3 1 3)
Find the eigenvectors for -1, 2, 8.
Chapter 12 Solutions
Numerical Analysis
Ch. 12.1 - Find the characteristic polynomial and the...Ch. 12.1 - Find the characteristic polynomial and the...Ch. 12.1 - Prob. 3ECh. 12.1 - Prove that a square matrix and its transpose have...Ch. 12.1 - Assume that A is a 33 matrix with the given...Ch. 12.1 - Assume that A is a 33 matrix with the given...Ch. 12.1 - Prob. 7ECh. 12.1 - Prob. 8ECh. 12.1 - Let A=[ 1243 ] . (a) Find all eigenvalues and...Ch. 12.1 - Let A=[ 2113 ] . Carry out the steps of Exercise 9...
Ch. 12.1 - If A is a 66 matrix with eigenvalues -6, -3, 1, 2,...Ch. 12.1 - Prob. 1CPCh. 12.1 - Prob. 2CPCh. 12.1 - Prob. 3CPCh. 12.1 - Prob. 4CPCh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Call a square matrix stochastic if the entries of...Ch. 12.2 - Prob. 5ECh. 12.2 - (a) Show that the determinant of a matrix in real...Ch. 12.2 - Decide whether the preliminary version of the QR...Ch. 12.2 - Prob. 8ECh. 12.2 - Prob. 1CPCh. 12.2 - Prob. 2CPCh. 12.2 - Prob. 3CPCh. 12.2 - Prob. 4CPCh. 12.2 - Prob. 5CPCh. 12.2 - Prob. 6CPCh. 12.2 - Prob. 7CPCh. 12.2 - Verify the page rank eigenvector p for Figure...Ch. 12.2 - Prob. 2SACh. 12.2 - Prob. 3SACh. 12.2 - Prob. 4SACh. 12.2 - Set q=0.15 . Suppose that Page 2 in the Figure...Ch. 12.2 - Prob. 6SACh. 12.2 - Design your own network, compute page ranks, and...Ch. 12.3 - Find the SVD of the following symmetric matrices...Ch. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - (a) Prove that the ui , as defined in Theorem...Ch. 12.3 - Prove that for any constants a and b, the nonzero...Ch. 12.3 - Prob. 6ECh. 12.3 - Prob. 7ECh. 12.3 - Prove that for any constants a and b, the nonzero...Ch. 12.4 - Use MATLAbS svd command to find the best rank-one...Ch. 12.4 - Prob. 2CPCh. 12.4 - Find the best least squares approximating line for...Ch. 12.4 - Find the best least squares approximating plane...Ch. 12.4 - Prob. 5CPCh. 12.4 - Continuing Computer Problem 5, add code to find...Ch. 12.4 - Use the code developed in Computer Problem 6 to...Ch. 12.4 - Import a photo, using MATLABs imread command. Use...
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- 0, 1, 1, 3, 5, 11,. A string of numbers starting with the numbers 0 and 1 is given above. For k> = 3, the previous two terms in the series The relation with the term can be expressed as ak=ak-1+2*ak-2 Using the eigenvalue vectors of the matrix A, calculate the 20th term of the array.arrow_forwardApply the power method anyway with th e given initial vector x0, performing eight iterations in each case. Compute the exact eigenvalues and eigenvectors and explain what is happening.arrow_forwardFind the matrix to which P converges as n increases. n ان د ان 0.44444 0.44444 -* The matrix converges to 0.55555 0.55555 (Type an integer or decimal for each matrix element. Round to five decimal places as needed.)arrow_forward
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