Draw Gershgorin Circles that contain the eigenvalues of A.

Learning Goal: I’m working on a numerical analysis project and need an explanation and answer to help me learn.

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
“1” on it. The super diagonal (the diagonal above the main diagonal) has “8” on it. The subdiagonal (below the
main diagonal) has “2”Rest of the matrix is “zero”. Our starting vector xo has all ones. Our tolerance is 0.01.

1Draw Gershgorin Circles that contain the eigenvalues of A.
Mark each radius properly.

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

3With a starting vector xo= [1 1 1 1….1]T, apply the usual power method to estimate 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____________

5Use the deflation technique discussed in class or in the book, to compute the second largest eigenvalue.
Tolerance = 0.01Print the second largest eigenvalue with 4 decimals: _________________

6) Print the number of iterations required for the second largest eigenvalue 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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