| The symmetric quadratic eigenvalue problem l2M+lC+K u=0, where M, C, and K are given n x n matrices and (lambda, u) is an eigenpair, arises in a wide variety of practical applications including vibration, acoustic, and noise control analysis [31]. In most practical applications, the problem is often of a very large dimension. Because of the nonlinearity and the large dimension of the coefficient matrices, the problem is extremely hard to solve numerically, and even the state-of-art computational techniques, such as the Jacobi-Davidson method, are capable of computing only a few extremal eigenvalues and eigenvectors [1,2,3]. There are engineering applications that require the computation of only some of the eigenvalues lying within an interval. In this dissertation, a new Hybrid method combining the parametrized Newton-Secant method described in Chapter 4 with the Jacobi-Davidson method is proposed to compute an eigenpair of a symmetric quadratic pencil within an interval. The experimental results in Chapter 4 & 5 show that the Parametrized Newton-Secant method and Hybrid method are much faster than other existing methods described in Chapter 3. |
