Solving Symmetric-Definite Quadratic $\lambda $-Matrix Problems without Factorization
David Sanborn Scott, Robert C. Ward · SIAM Journal on Scientific and Statistical Computing · 1982
Algorithms are presented for computing some of the eigenvalues and their associated eigenvectors of the quadratic $\lambda $-matrix$M\lambda ^2 + C\lambda + K$. M, C and K are assumed to have special symmetrytype properties which insure that theory analogous to the standard symmetric eigenproblem exists. The algorithms are based on a generalization of the Rayleigh quotient and the, Lanczos method for computing eigenpairs of standard symmetric eigenproblems. Monotone quadratic convergence of the basic method is proved. Test examples are presented.