CAS EXPERIMENT. Power Method with Scaling. Shifting. (a) Write a program for 11 X 11
Chapter 20, Problem 20.1.136(choose chapter or problem)
CAS EXPERIMENT. Power Method with Scaling. Shifting. (a) Write a program for \(n \times n\) matrices that prints every step. Apply it to the (nonsymmetric!) matrix (20 steps), starting from \(\left[\begin{array}{lll}1 & 1 & 1\end{array}\right]^{\top}\).
\(A=\left[\begin{array}{rrr}15 & 12 & 3 \\18 & 44 & 18 \\-19 & -36 & -7\end{array}\right]\).
(b) Experiment in (a) with shifting. Which shift do you find optimal?
(c) Write a program as in (a) but for symmetric matrices that prints vectors, scaled vectors, q, and \(\delta\). Apply it to the matrix in Prob. 6.
(d) Find a (nonsymmetric) matrix for which \(\delta\) in (2) is no longer an error bound.
Text Transcription:
n times n
[1 1 1]^T
A=[15 12 3
18 44 18
-19 -36 -7]
delta
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