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 sub–diagonal (below the
main diagonal) has “2”. Rest of the matrix is “zero”. Our starting vector xo has all ones. Our tolerance is 0.01.
1) Draw 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: _______________
3) With 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. ____________
5) Use the deflation technique discussed in class or in the book, to compute the second largest eigenvalue.
Tolerance = 0.01. Print 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.
Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.
You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.
Read moreEach paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.
Read moreThanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.
Read moreYour email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.
Read moreBy sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.
Read more
Recent Comments