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## Example

We continue to use the example introduced in §2.1 and Figure 2.1. We again consider the case with arbitrary masses , and zero damping constants . This simplifies the equations of motion to . As in §2.3.8 we solve the equations of motion by substituting , where is a constant vector and is a constant scalar to be determined. This leads to . Letting , where the Cholesky factor , we see that we need to compute the eigenvalues of the symmetric tridiagonal matrix shown in equation (2.2).

Now we note that the stiffness matrix can be factored as , where and This lets us write Therefore, the singular values of the bidiagonal matrix are the square roots of the eigenvalues of , and the left singular vectors of are the eigenvectors of .

Bidiagonal matrices have particularly fast and efficient SVD algorithms.     Next: Non-Hermitian Eigenproblems  J. Demmel Up: Singular Value Decomposition  J. Previous: Related Singular Value Problems   Contents   Index
Susan Blackford 2000-11-20