Unformatted text preview: λ k = α + 2 β cos ± kπ n + 1 ² (verify this identity if you use it). You can also use Gershgorin’s three theorems do generate a matrix with various distributions on eigenvalues. One such theorem is in the text on p. 320. Numerical Mathematics by Quarteroni, Sacco and Saleri has a statement of all three theorems. You can also generate a symmetric matrix A = Q Λ Q T by choosing the eigenvalues and then constructing an orthogonal matrix Q , e.g., random orthogonal. The solution should include the subroutine or Mﬁle as well as a test driver and the appropriate documentation. The test driver and documentation should include a description of the testing you did and the necessary code to repeat it. Most important in the solution is, of course, you discussion of how you evaluated your code and what it indicated about using Jacobi methods to solve the symmetric eigenvalue problem. 1...
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 Fall '06
 gallivan

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