Posted: February 23rd, 2022

Power Method

This project computes the two largest eigenvalues of a 50×50 matrix. You will use the usual Power Method to compute the largest eigenvalue. For the next largest eigenvalue, you can use an “Annihilation or Deflation or Shifting technique” discussed in class and also in our book. The matrix A is tridiagonal. Its main diagonal has ones on it. The super diagonal (the diagonal above the main diagonal) has negative-ones on it. The sub-diagonal (below the main diagonal) has negative-ones also. Our starting vector x_o has all ones. Our tolerance is 0.01.

Turn in the following on one page

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

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

2) Based on part (1), what is the spectral radius of A. Print your answer here: _______________

3) With a starting vector x_o= [1  1  1  1….1]^T, apply the usual power method to estimate l_max , the dominant-

     eigenvalue of matrix A. Use a tolerance of 0.01.  Print your answer with 4 decimals: ____________

4) Print the number of iterations required to converge. ____________

5) Use the deflation technique discussed in class to compute the second largest eigenvalue. Tolerance = 0.01

     Print the second largest eigenvalue with 4 decimals: _________________

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

7) Print your computer program here. As discussed in class, the main body of your program is 3 lines, so your

    program should not be long.

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