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 ,
Bidiagonal matrices have particularly fast and efficient SVD algorithms.