I have used power method to find the dominant Eigen value and corresponding normalized Eigen vector of the 7x7 matrix I used in HW1
A = X(0) = [1 1 1 1 1 1 1] A = X(0) = [1 1 1 1 1 1 1] |
Iteration number 1 Y(1)=AX(0) C = max(Y(1)) = 14.621602 X(1) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 2 Y(2)=AX(1) C = max(Y(2)) = 33.548327 X(2) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 3 Y(3)=AX(2) C = max(Y(3)) = 33.548327 X(3) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 4 Y(4)=AX(3) C = max(Y(4)) = 33.548327 X(4) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 5 Y(5)=AX(4) C = max(Y(5)) = 33.548327 X(5) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 6 Y(6)=AX(5) C = max(Y(6)) = 33.548327 X(6) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 7 Y(7)=AX(6) C = max(Y(7)) = 33.548327 X(7) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 8 Y(8)=AX(7) C = max(Y(8)) = 33.548327 X(8) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 9 Y(9)=AX(8) C = max(Y(9)) = 33.548327 X(9) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 10 Y(10)=AX(9) C = max(Y(10)) = 33.548327 X(10) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 11 Y(11)=AX(10) C = max(Y(11)) = 33.548327 X(11) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 12 Y(12)=AX(11) C = max(Y(12)) = 33.548327 X(12) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 13 Y(13)=AX(12) C = max(Y(13)) = 33.548327 X(13) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 14 Y(14)=AX(13) C = max(Y(14)) = 33.548327 X(14) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 15 Y(15)=AX(14) C = max(Y(15)) = 33.548327 X(15) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 1 Y(1)=AX(0) C = max(Y(1)) = 14.621602 X(1) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 2 Y(2)=AX(1) C = max(Y(2)) = 33.548327 X(2) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 3 Y(3)=AX(2) C = max(Y(3)) = 33.548327 X(3) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 4 Y(4)=AX(3) C = max(Y(4)) = 33.548327 X(4) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 5 Y(5)=AX(4) C = max(Y(5)) = 33.548327 X(5) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 6 Y(6)=AX(5) C = max(Y(6)) = 33.548327 X(6) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 7 Y(7)=AX(6) C = max(Y(7)) = 33.548327 X(7) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 8 Y(8)=AX(7) C = max(Y(8)) = 33.548327 X(8) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 9 Y(9)=AX(8) C = max(Y(9)) = 33.548327 X(9) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 10 Y(10)=AX(9) C = max(Y(10)) = 33.548327 X(10) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 11 Y(11)=AX(10) C = max(Y(11)) = 33.548327 X(11) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 12 Y(12)=AX(11) C = max(Y(12)) = 33.548327 X(12) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 13 Y(13)=AX(12) C = max(Y(13)) = 33.548327 X(13) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 14 Y(14)=AX(13) C = max(Y(14)) = 33.548327 X(14) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] Iteration number 15 Y(15)=AX(14) C = max(Y(15)) = 33.548327 X(15) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413 1.0] |
__main__:2: DeprecationWarning: The default norm will be changing from p='frob' to p=2. Use p='frob' explicitly to continue calculating the Frobenius norm. See http://trac.sagemath.org/13643 for details. Dominant Eigen Value = 33.5483274572 Normalized corresponding Eigen Vector is: X^T . A . X = [33.5483274572] __main__:2: DeprecationWarning: The default norm will be changing from p='frob' to p=2. Use p='frob' explicitly to continue calculating the Frobenius norm. See http://trac.sagemath.org/13643 for details. Dominant Eigen Value = 33.5483274572 Normalized corresponding Eigen Vector is: X^T . A . X = [33.5483274572] |
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