Posted: February 23rd, 2022

Power Method

This undertaking computes the 2 largest eigenvalues of a 50×50 matrix. You’ll use the standard Power Method to compute the biggest eigenvalue. For the following largest eigenvalue, you need to use an “Annihilation or Deflation or Shifting approach” mentioned in school and in addition in our ebook. The matrix A is tridiagonal. Its primary diagonal has ones on it. The tremendous diagonal (the diagonal above the primary diagonal) has negative-ones on it. The sub-diagonal (under the primary diagonal) has negative-ones additionally. Our beginning vector x_o has all ones. Our tolerance is zero.01.

Flip within the following on one web page

1) Draw Gershgorin Circles that comprise the eigenvalues of A.

     Use “insert” from the menu to find and draw circles.

2) Primarily based on half (1), what’s the spectral radius of A. Print your reply right here: _______________

three) With a beginning vector x_o= [1  1  1  1….1]^T, apply the standard energy methodology to estimate l_max , the dominant-

     eigenvalue of matrix A. Use a tolerance of zero.01.  Print your reply with four decimals: ____________

four) Print the variety of iterations required to converge. ____________

5) Use the deflation approach mentioned in school to compute the second largest eigenvalue. Tolerance = zero.01

     Print the second largest eigenvalue with four decimals: _________________

6) Print the variety of iterations required to converge.  ___________

7) Print your pc program right here. As mentioned in school, the primary physique of your program is three traces, so your

    program shouldn’t be lengthy.

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