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b) Consider the matrix UTMUTM U 21 5 7 A = -1 MUTM U TMUTM -4 20 UT i. Compute the dominant eigenvalue, dy and the corresponding eigen- vector x for the matrix A using power method starting with x0) = (1, 1, 1)" and stop the iterations when |m+1- mel < 0.05. AUTM TMUTM ii. Determine the smallest eigenvalue, Ag for matrix A by using shifted UTM power method based on the results in (i). Start the iteration with initial vector x) = (1,0,0)" and stop the iterations when ||x*+1) – x")|l < 0.05.

b) Consider the matrix UTMUTM U 21 5 7 A = -1 MUTM U TMUTM -4 20 UT i. Compute the dominant eigenvalue, dy and the corresponding eigen- vector x for the matrix A using power method starting with x0) = (1, 1, 1)" and stop the iterations when |m+1- mel < 0.05. AUTM TMUTM ii. Determine the smallest eigenvalue, Ag for matrix A by using shifted UTM power method based on the results in (i). Start the iteration with initial vector x) = (1,0,0)" and stop the iterations when ||x*+1) – x")|l < 0.05.

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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b) Consider the matrix TM UTM UTM UTM -1 21 A = OTM UTM 7TMUTM UTM 4 i. Compute the dominant eigenvalue, di and the corresponding eigen- -4 20 UT vector x1 for the matrix A using power method starting with x0) = (1, 1, 1)" and stop the iterations when |mg+1 – mel < 0.05. AUTM %3D ii. Determine the smallest eigenvalue, Az for matrix A by using shifted power method based on the results in (i). Start the iteration with initial vector x) = (1,0,0)" and stop the iterations when ||x*+1) – x*)|| < 0.05. TM UTM UTM (k) %3D
Transcribed Image Text:b) Consider the matrix TM UTM UTM UTM -1 21 A = OTM UTM 7TMUTM UTM 4 i. Compute the dominant eigenvalue, di and the corresponding eigen- -4 20 UT vector x1 for the matrix A using power method starting with x0) = (1, 1, 1)" and stop the iterations when |mg+1 – mel < 0.05. AUTM %3D ii. Determine the smallest eigenvalue, Az for matrix A by using shifted power method based on the results in (i). Start the iteration with initial vector x) = (1,0,0)" and stop the iterations when ||x*+1) – x*)|| < 0.05. TM UTM UTM (k) %3D
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